{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0001","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"A\":[2,3],\"B\":[0,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 3], 1/7, 37/49, 1/49, 37/343, 否)","explanation_zh":"Wave4根節點核對=([2, 3], [0, 3], 1/7, 37/49, 1/49, 37/343, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276001,"parameters":{"masses":[[36,49],[6,49],[6,49],[1,49]],"A":[2,3],"B":[0,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[0,3],\"masses\":[[36,49],[6,49],[6,49],[1,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0002","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 2/7, 1/7, 2/49, 2/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 2/7, 1/7, 2/49, 2/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276002,"parameters":{"masses":[[30,49],[5,49],[12,49],[2,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[30,49],[5,49],[12,49],[2,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0003","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 3/7, 1/7, 3/49, 3/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 3/7, 1/7, 3/49, 3/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276003,"parameters":{"masses":[[24,49],[4,49],[18,49],[3,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[24,49],[4,49],[18,49],[3,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0004","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 4/7, 1/7, 4/49, 4/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 4/7, 1/7, 4/49, 4/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276004,"parameters":{"masses":[[18,49],[3,49],[24,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[18,49],[3,49],[24,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0005","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"A\":[2,3],\"B\":[0,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 3], 5/7, 17/49, 5/49, 85/343, 否)","explanation_zh":"Wave4根節點核對=([2, 3], [0, 3], 5/7, 17/49, 5/49, 85/343, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276005,"parameters":{"masses":[[12,49],[2,49],[30,49],[5,49]],"A":[2,3],"B":[0,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[0,3],\"masses\":[[12,49],[2,49],[30,49],[5,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0006","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 1/7, 2/7, 2/49, 2/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 1/7, 2/7, 2/49, 2/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276006,"parameters":{"masses":[[30,49],[12,49],[5,49],[2,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[30,49],[12,49],[5,49],[2,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0007","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 2/7, 2/7, 4/49, 4/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 2/7, 2/7, 4/49, 4/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276007,"parameters":{"masses":[[25,49],[10,49],[10,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[25,49],[10,49],[10,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0008","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 3/7, 2/7, 6/49, 6/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 3/7, 2/7, 6/49, 6/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276008,"parameters":{"masses":[[20,49],[8,49],[15,49],[6,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[20,49],[8,49],[15,49],[6,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0009","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"A\":[2,3],\"B\":[0,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 3], 4/7, 23/49, 8/49, 92/343, 否)","explanation_zh":"Wave4根節點核對=([2, 3], [0, 3], 4/7, 23/49, 8/49, 92/343, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276009,"parameters":{"masses":[[15,49],[6,49],[20,49],[8,49]],"A":[2,3],"B":[0,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[0,3],\"masses\":[[15,49],[6,49],[20,49],[8,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0010","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 5/7, 2/7, 10/49, 10/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 5/7, 2/7, 10/49, 10/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276010,"parameters":{"masses":[[10,49],[4,49],[25,49],[10,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[10,49],[4,49],[25,49],[10,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0011","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 1/7, 3/7, 3/49, 3/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 1/7, 3/7, 3/49, 3/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276011,"parameters":{"masses":[[24,49],[18,49],[4,49],[3,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[24,49],[18,49],[4,49],[3,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0012","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 2/7, 3/7, 6/49, 6/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 2/7, 3/7, 6/49, 6/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276012,"parameters":{"masses":[[20,49],[15,49],[8,49],[6,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[20,49],[15,49],[8,49],[6,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0013","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"A\":[2,3],\"B\":[0,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 3], 3/7, 25/49, 9/49, 75/343, 否)","explanation_zh":"Wave4根節點核對=([2, 3], [0, 3], 3/7, 25/49, 9/49, 75/343, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276013,"parameters":{"masses":[[16,49],[12,49],[12,49],[9,49]],"A":[2,3],"B":[0,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[0,3],\"masses\":[[16,49],[12,49],[12,49],[9,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0014","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 4/7, 3/7, 12/49, 12/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 4/7, 3/7, 12/49, 12/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276014,"parameters":{"masses":[[12,49],[9,49],[16,49],[12,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[9,49],[16,49],[12,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0015","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 5/7, 3/7, 15/49, 15/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 5/7, 3/7, 15/49, 15/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276015,"parameters":{"masses":[[8,49],[6,49],[20,49],[15,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[8,49],[6,49],[20,49],[15,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0016","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 1/7, 4/7, 4/49, 4/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 1/7, 4/7, 4/49, 4/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276016,"parameters":{"masses":[[18,49],[24,49],[3,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[18,49],[24,49],[3,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0017","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"A\":[2,3],\"B\":[0,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 3], 2/7, 23/49, 8/49, 46/343, 否)","explanation_zh":"Wave4根節點核對=([2, 3], [0, 3], 2/7, 23/49, 8/49, 46/343, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276017,"parameters":{"masses":[[15,49],[20,49],[6,49],[8,49]],"A":[2,3],"B":[0,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[0,3],\"masses\":[[15,49],[20,49],[6,49],[8,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0018","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 3/7, 4/7, 12/49, 12/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 3/7, 4/7, 12/49, 12/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276018,"parameters":{"masses":[[12,49],[16,49],[9,49],[12,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[16,49],[9,49],[12,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0019","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 4/7, 4/7, 16/49, 16/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 4/7, 4/7, 16/49, 16/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276019,"parameters":{"masses":[[9,49],[12,49],[12,49],[16,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[9,49],[12,49],[12,49],[16,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0020","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 5/7, 4/7, 20/49, 20/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 5/7, 4/7, 20/49, 20/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276020,"parameters":{"masses":[[6,49],[8,49],[15,49],[20,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[6,49],[8,49],[15,49],[20,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0021","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"A\":[2,3],\"B\":[0,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 3], 1/7, 17/49, 5/49, 17/343, 否)","explanation_zh":"Wave4根節點核對=([2, 3], [0, 3], 1/7, 17/49, 5/49, 17/343, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276021,"parameters":{"masses":[[12,49],[30,49],[2,49],[5,49]],"A":[2,3],"B":[0,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[0,3],\"masses\":[[12,49],[30,49],[2,49],[5,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0022","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 2/7, 5/7, 10/49, 10/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 2/7, 5/7, 10/49, 10/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276022,"parameters":{"masses":[[10,49],[25,49],[4,49],[10,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[10,49],[25,49],[4,49],[10,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0023","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 3/7, 5/7, 15/49, 15/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 3/7, 5/7, 15/49, 15/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276023,"parameters":{"masses":[[8,49],[20,49],[6,49],[15,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[8,49],[20,49],[6,49],[15,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0024","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [1, 3], 4/7, 5/7, 20/49, 20/49, 是)","explanation_zh":"Wave4根節點核對=([2, 3], [1, 3], 4/7, 5/7, 20/49, 20/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276024,"parameters":{"masses":[[6,49],[15,49],[8,49],[20,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[6,49],[15,49],[8,49],[20,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0025","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-audit；資料={\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"A\":[2,3],\"B\":[0,3]}。請依 [A,B,P_A,P_B,P_intersection,product,independent] 欄序回答。","answer":{"kind":"expression","value":"([2, 3], [0, 3], 5/7, 29/49, 25/49, 145/343, 否)","explanation_zh":"Wave4根節點核對=([2, 3], [0, 3], 5/7, 29/49, 25/49, 145/343, 否)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-audit","seed":202610276025,"parameters":{"masses":[[4,49],[10,49],[10,49],[25,49]],"A":[2,3],"B":[0,3],"domain":"Exact_finite_event_independence","operation":"eventind-audit","semantic_template":"qf-mod27-eventind-audit/{\"A\":[2,3],\"B\":[0,3],\"masses\":[[4,49],[10,49],[10,49],[25,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0026","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 1/7, 1/49, 1/7, 是, 是)","explanation_zh":"Wave4根節點核對=(1/7, 1/7, 1/49, 1/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276026,"parameters":{"masses":[[36,49],[6,49],[6,49],[1,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[36,49],[6,49],[6,49],[1,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0027","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 1/7, 2/49, 2/7, 是, 是)","explanation_zh":"Wave4根節點核對=(2/7, 1/7, 2/49, 2/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276027,"parameters":{"masses":[[30,49],[5,49],[12,49],[2,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[30,49],[5,49],[12,49],[2,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0028","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 1/7, 3/49, 3/7, 是, 是)","explanation_zh":"Wave4根節點核對=(3/7, 1/7, 3/49, 3/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276028,"parameters":{"masses":[[24,49],[4,49],[18,49],[3,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[24,49],[4,49],[18,49],[3,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0029","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 1/7, 4/49, 4/7, 是, 是)","explanation_zh":"Wave4根節點核對=(4/7, 1/7, 4/49, 4/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276029,"parameters":{"masses":[[18,49],[3,49],[24,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[18,49],[3,49],[24,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0030","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 1/7, 5/49, 5/7, 是, 是)","explanation_zh":"Wave4根節點核對=(5/7, 1/7, 5/49, 5/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276030,"parameters":{"masses":[[12,49],[2,49],[30,49],[5,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[2,49],[30,49],[5,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0031","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 2/7, 2/49, 1/7, 是, 是)","explanation_zh":"Wave4根節點核對=(1/7, 2/7, 2/49, 1/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276031,"parameters":{"masses":[[30,49],[12,49],[5,49],[2,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[30,49],[12,49],[5,49],[2,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0032","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 2/7, 4/49, 2/7, 是, 是)","explanation_zh":"Wave4根節點核對=(2/7, 2/7, 4/49, 2/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276032,"parameters":{"masses":[[25,49],[10,49],[10,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[25,49],[10,49],[10,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0033","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 2/7, 6/49, 3/7, 是, 是)","explanation_zh":"Wave4根節點核對=(3/7, 2/7, 6/49, 3/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276033,"parameters":{"masses":[[20,49],[8,49],[15,49],[6,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[20,49],[8,49],[15,49],[6,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0034","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 2/7, 8/49, 4/7, 是, 是)","explanation_zh":"Wave4根節點核對=(4/7, 2/7, 8/49, 4/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276034,"parameters":{"masses":[[15,49],[6,49],[20,49],[8,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[15,49],[6,49],[20,49],[8,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0035","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 2/7, 10/49, 5/7, 是, 是)","explanation_zh":"Wave4根節點核對=(5/7, 2/7, 10/49, 5/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276035,"parameters":{"masses":[[10,49],[4,49],[25,49],[10,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[10,49],[4,49],[25,49],[10,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0036","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 3/7, 3/49, 1/7, 是, 是)","explanation_zh":"Wave4根節點核對=(1/7, 3/7, 3/49, 1/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276036,"parameters":{"masses":[[24,49],[18,49],[4,49],[3,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[24,49],[18,49],[4,49],[3,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0037","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 3/7, 6/49, 2/7, 是, 是)","explanation_zh":"Wave4根節點核對=(2/7, 3/7, 6/49, 2/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276037,"parameters":{"masses":[[20,49],[15,49],[8,49],[6,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[20,49],[15,49],[8,49],[6,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0038","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 3/7, 9/49, 3/7, 是, 是)","explanation_zh":"Wave4根節點核對=(3/7, 3/7, 9/49, 3/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276038,"parameters":{"masses":[[16,49],[12,49],[12,49],[9,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[16,49],[12,49],[12,49],[9,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0039","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 3/7, 12/49, 4/7, 是, 是)","explanation_zh":"Wave4根節點核對=(4/7, 3/7, 12/49, 4/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276039,"parameters":{"masses":[[12,49],[9,49],[16,49],[12,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[9,49],[16,49],[12,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0040","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 3/7, 15/49, 5/7, 是, 是)","explanation_zh":"Wave4根節點核對=(5/7, 3/7, 15/49, 5/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276040,"parameters":{"masses":[[8,49],[6,49],[20,49],[15,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[8,49],[6,49],[20,49],[15,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0041","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 4/7, 4/49, 1/7, 是, 是)","explanation_zh":"Wave4根節點核對=(1/7, 4/7, 4/49, 1/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276041,"parameters":{"masses":[[18,49],[24,49],[3,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[18,49],[24,49],[3,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0042","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 4/7, 8/49, 2/7, 是, 是)","explanation_zh":"Wave4根節點核對=(2/7, 4/7, 8/49, 2/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276042,"parameters":{"masses":[[15,49],[20,49],[6,49],[8,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[15,49],[20,49],[6,49],[8,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0043","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 4/7, 12/49, 3/7, 是, 是)","explanation_zh":"Wave4根節點核對=(3/7, 4/7, 12/49, 3/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276043,"parameters":{"masses":[[12,49],[16,49],[9,49],[12,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[16,49],[9,49],[12,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0044","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 4/7, 16/49, 4/7, 是, 是)","explanation_zh":"Wave4根節點核對=(4/7, 4/7, 16/49, 4/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276044,"parameters":{"masses":[[9,49],[12,49],[12,49],[16,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[9,49],[12,49],[12,49],[16,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0045","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 4/7, 20/49, 5/7, 是, 是)","explanation_zh":"Wave4根節點核對=(5/7, 4/7, 20/49, 5/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276045,"parameters":{"masses":[[6,49],[8,49],[15,49],[20,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[6,49],[8,49],[15,49],[20,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0046","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 5/7, 5/49, 1/7, 是, 是)","explanation_zh":"Wave4根節點核對=(1/7, 5/7, 5/49, 1/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276046,"parameters":{"masses":[[12,49],[30,49],[2,49],[5,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[30,49],[2,49],[5,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0047","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 5/7, 10/49, 2/7, 是, 是)","explanation_zh":"Wave4根節點核對=(2/7, 5/7, 10/49, 2/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276047,"parameters":{"masses":[[10,49],[25,49],[4,49],[10,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[10,49],[25,49],[4,49],[10,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0048","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 5/7, 15/49, 3/7, 是, 是)","explanation_zh":"Wave4根節點核對=(3/7, 5/7, 15/49, 3/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276048,"parameters":{"masses":[[8,49],[20,49],[6,49],[15,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[8,49],[20,49],[6,49],[15,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0049","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 5/7, 20/49, 4/7, 是, 是)","explanation_zh":"Wave4根節點核對=(4/7, 5/7, 20/49, 4/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276049,"parameters":{"masses":[[6,49],[15,49],[8,49],[20,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[6,49],[15,49],[8,49],[20,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0050","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-conditional-equivalence；資料={\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [P_A,P_B,P_intersection,P_A_given_B,conditional_equal,independent] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 5/7, 25/49, 5/7, 是, 是)","explanation_zh":"Wave4根節點核對=(5/7, 5/7, 25/49, 5/7, 是, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-conditional-equivalence","seed":202610276050,"parameters":{"masses":[[4,49],[10,49],[10,49],[25,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-conditional-equivalence","semantic_template":"qf-mod27-eventind-conditional-equivalence/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[4,49],[10,49],[10,49],[25,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0051","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[36,49],[6,49],[6,49],[1,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 6/7, 6/49, 6/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 6/7, 6/49, 6/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276051,"parameters":{"masses":[[36,49],[6,49],[6,49],[1,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[36,49],[6,49],[6,49],[1,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0052","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[30,49],[5,49],[12,49],[2,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 5/7, 5/49, 5/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 5/7, 5/49, 5/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276052,"parameters":{"masses":[[30,49],[5,49],[12,49],[2,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[30,49],[5,49],[12,49],[2,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0053","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[24,49],[4,49],[18,49],[3,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 4/7, 4/49, 4/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 4/7, 4/49, 4/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276053,"parameters":{"masses":[[24,49],[4,49],[18,49],[3,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[24,49],[4,49],[18,49],[3,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0054","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[18,49],[3,49],[24,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 3/7, 3/49, 3/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 3/7, 3/49, 3/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276054,"parameters":{"masses":[[18,49],[3,49],[24,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[18,49],[3,49],[24,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0055","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[12,49],[2,49],[30,49],[5,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 2/7, 2/49, 2/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 2/7, 2/49, 2/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276055,"parameters":{"masses":[[12,49],[2,49],[30,49],[5,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[2,49],[30,49],[5,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0056","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[30,49],[12,49],[5,49],[2,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 6/7, 12/49, 12/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 6/7, 12/49, 12/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276056,"parameters":{"masses":[[30,49],[12,49],[5,49],[2,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[30,49],[12,49],[5,49],[2,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0057","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[25,49],[10,49],[10,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 5/7, 10/49, 10/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 5/7, 10/49, 10/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276057,"parameters":{"masses":[[25,49],[10,49],[10,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[25,49],[10,49],[10,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0058","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[20,49],[8,49],[15,49],[6,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 4/7, 8/49, 8/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 4/7, 8/49, 8/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276058,"parameters":{"masses":[[20,49],[8,49],[15,49],[6,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[20,49],[8,49],[15,49],[6,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0059","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[15,49],[6,49],[20,49],[8,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 3/7, 6/49, 6/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 3/7, 6/49, 6/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276059,"parameters":{"masses":[[15,49],[6,49],[20,49],[8,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[15,49],[6,49],[20,49],[8,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0060","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[10,49],[4,49],[25,49],[10,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 2/7, 4/49, 4/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 2/7, 4/49, 4/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276060,"parameters":{"masses":[[10,49],[4,49],[25,49],[10,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[10,49],[4,49],[25,49],[10,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0061","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[24,49],[18,49],[4,49],[3,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 6/7, 18/49, 18/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 6/7, 18/49, 18/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276061,"parameters":{"masses":[[24,49],[18,49],[4,49],[3,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[24,49],[18,49],[4,49],[3,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0062","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[20,49],[15,49],[8,49],[6,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 5/7, 15/49, 15/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 5/7, 15/49, 15/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276062,"parameters":{"masses":[[20,49],[15,49],[8,49],[6,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[20,49],[15,49],[8,49],[6,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0063","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[16,49],[12,49],[12,49],[9,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 4/7, 12/49, 12/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 4/7, 12/49, 12/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276063,"parameters":{"masses":[[16,49],[12,49],[12,49],[9,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[16,49],[12,49],[12,49],[9,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0064","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[12,49],[9,49],[16,49],[12,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 3/7, 9/49, 9/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 3/7, 9/49, 9/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276064,"parameters":{"masses":[[12,49],[9,49],[16,49],[12,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[9,49],[16,49],[12,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0065","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[8,49],[6,49],[20,49],[15,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 2/7, 6/49, 6/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 2/7, 6/49, 6/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276065,"parameters":{"masses":[[8,49],[6,49],[20,49],[15,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[8,49],[6,49],[20,49],[15,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0066","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[18,49],[24,49],[3,49],[4,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 6/7, 24/49, 24/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 6/7, 24/49, 24/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276066,"parameters":{"masses":[[18,49],[24,49],[3,49],[4,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[18,49],[24,49],[3,49],[4,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0067","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[15,49],[20,49],[6,49],[8,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 5/7, 20/49, 20/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 5/7, 20/49, 20/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276067,"parameters":{"masses":[[15,49],[20,49],[6,49],[8,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[15,49],[20,49],[6,49],[8,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0068","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[12,49],[16,49],[9,49],[12,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 4/7, 16/49, 16/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 4/7, 16/49, 16/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276068,"parameters":{"masses":[[12,49],[16,49],[9,49],[12,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[16,49],[9,49],[12,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0069","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[9,49],[12,49],[12,49],[16,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 3/7, 12/49, 12/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 3/7, 12/49, 12/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276069,"parameters":{"masses":[[9,49],[12,49],[12,49],[16,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[9,49],[12,49],[12,49],[16,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0070","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[6,49],[8,49],[15,49],[20,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 2/7, 8/49, 8/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 2/7, 8/49, 8/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276070,"parameters":{"masses":[[6,49],[8,49],[15,49],[20,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[6,49],[8,49],[15,49],[20,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0071","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[12,49],[30,49],[2,49],[5,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 6/7, 30/49, 30/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 6/7, 30/49, 30/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276071,"parameters":{"masses":[[12,49],[30,49],[2,49],[5,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[12,49],[30,49],[2,49],[5,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0072","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[10,49],[25,49],[4,49],[10,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 5/7, 25/49, 25/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 5/7, 25/49, 25/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276072,"parameters":{"masses":[[10,49],[25,49],[4,49],[10,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[10,49],[25,49],[4,49],[10,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0073","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[8,49],[20,49],[6,49],[15,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 4/7, 20/49, 20/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 4/7, 20/49, 20/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276073,"parameters":{"masses":[[8,49],[20,49],[6,49],[15,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[8,49],[20,49],[6,49],[15,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0074","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[6,49],[15,49],[8,49],[20,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 3/7, 15/49, 15/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 3/7, 15/49, 15/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276074,"parameters":{"masses":[[6,49],[15,49],[8,49],[20,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[6,49],[15,49],[8,49],[20,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0075","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-complement；資料={\"masses\":[[4,49],[10,49],[10,49],[25,49]],\"A\":[2,3],\"B\":[1,3]}。請依 [original_independent,A_complement,P_complement,P_complement_intersection_B,product,complement_independent] 欄序回答。","answer":{"kind":"expression","value":"(是, [0, 1], 2/7, 10/49, 10/49, 是)","explanation_zh":"Wave4根節點核對=(是, [0, 1], 2/7, 10/49, 10/49, 是)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-complement","seed":202610276075,"parameters":{"masses":[[4,49],[10,49],[10,49],[25,49]],"A":[2,3],"B":[1,3],"domain":"Exact_finite_event_independence","operation":"eventind-complement","semantic_template":"qf-mod27-eventind-complement/{\"A\":[2,3],\"B\":[1,3],\"masses\":[[4,49],[10,49],[10,49],[25,49]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0076","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[36,49],[6,49],[6,49],[1,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276076,"parameters":{"masses":[[36,49],[6,49],[6,49],[1,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[36,49],[6,49],[6,49],[1,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0077","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[30,49],[5,49],[12,49],[2,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276077,"parameters":{"masses":[[30,49],[5,49],[12,49],[2,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[30,49],[5,49],[12,49],[2,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0078","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[24,49],[4,49],[18,49],[3,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276078,"parameters":{"masses":[[24,49],[4,49],[18,49],[3,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[24,49],[4,49],[18,49],[3,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0079","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[18,49],[3,49],[24,49],[4,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276079,"parameters":{"masses":[[18,49],[3,49],[24,49],[4,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[18,49],[3,49],[24,49],[4,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0080","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[12,49],[2,49],[30,49],[5,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276080,"parameters":{"masses":[[12,49],[2,49],[30,49],[5,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[12,49],[2,49],[30,49],[5,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0081","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[30,49],[12,49],[5,49],[2,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276081,"parameters":{"masses":[[30,49],[12,49],[5,49],[2,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[30,49],[12,49],[5,49],[2,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0082","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[25,49],[10,49],[10,49],[4,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276082,"parameters":{"masses":[[25,49],[10,49],[10,49],[4,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[25,49],[10,49],[10,49],[4,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0083","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[20,49],[8,49],[15,49],[6,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276083,"parameters":{"masses":[[20,49],[8,49],[15,49],[6,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[20,49],[8,49],[15,49],[6,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0084","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[15,49],[6,49],[20,49],[8,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276084,"parameters":{"masses":[[15,49],[6,49],[20,49],[8,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[15,49],[6,49],[20,49],[8,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0085","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[10,49],[4,49],[25,49],[10,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276085,"parameters":{"masses":[[10,49],[4,49],[25,49],[10,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[10,49],[4,49],[25,49],[10,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0086","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[24,49],[18,49],[4,49],[3,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276086,"parameters":{"masses":[[24,49],[18,49],[4,49],[3,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[24,49],[18,49],[4,49],[3,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0087","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[20,49],[15,49],[8,49],[6,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276087,"parameters":{"masses":[[20,49],[15,49],[8,49],[6,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[20,49],[15,49],[8,49],[6,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0088","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[16,49],[12,49],[12,49],[9,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276088,"parameters":{"masses":[[16,49],[12,49],[12,49],[9,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[16,49],[12,49],[12,49],[9,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0089","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[12,49],[9,49],[16,49],[12,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276089,"parameters":{"masses":[[12,49],[9,49],[16,49],[12,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[12,49],[9,49],[16,49],[12,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0090","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[8,49],[6,49],[20,49],[15,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276090,"parameters":{"masses":[[8,49],[6,49],[20,49],[15,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[8,49],[6,49],[20,49],[15,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0091","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[18,49],[24,49],[3,49],[4,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276091,"parameters":{"masses":[[18,49],[24,49],[3,49],[4,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[18,49],[24,49],[3,49],[4,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0092","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[15,49],[20,49],[6,49],[8,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276092,"parameters":{"masses":[[15,49],[20,49],[6,49],[8,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[15,49],[20,49],[6,49],[8,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0093","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[12,49],[16,49],[9,49],[12,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276093,"parameters":{"masses":[[12,49],[16,49],[9,49],[12,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[12,49],[16,49],[9,49],[12,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0094","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[9,49],[12,49],[12,49],[16,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276094,"parameters":{"masses":[[9,49],[12,49],[12,49],[16,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[9,49],[12,49],[12,49],[16,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0095","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[6,49],[8,49],[15,49],[20,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276095,"parameters":{"masses":[[6,49],[8,49],[15,49],[20,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[6,49],[8,49],[15,49],[20,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0096","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[12,49],[30,49],[2,49],[5,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(1/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276096,"parameters":{"masses":[[12,49],[30,49],[2,49],[5,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[12,49],[30,49],[2,49],[5,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0097","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[10,49],[25,49],[4,49],[10,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(2/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276097,"parameters":{"masses":[[10,49],[25,49],[4,49],[10,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[10,49],[25,49],[4,49],[10,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0098","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[8,49],[20,49],[6,49],[15,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(3/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276098,"parameters":{"masses":[[8,49],[20,49],[6,49],[15,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[8,49],[20,49],[6,49],[15,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0099","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[6,49],[15,49],[8,49],[20,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(4/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276099,"parameters":{"masses":[[6,49],[15,49],[8,49],[20,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[6,49],[15,49],[8,49],[20,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261027-r06-event-independence-0100","batch_id":"batch-20261014-advance-20261027-r06-event-independence-foundations","language":"zh-Hant","source_mko_ids":["mko-event-independence"],"title_zh":"事件獨立","stem_zh":"同一完整有限機率模型中的兩事件。操作=eventind-zero-probability-boundary；資料={\"masses\":[[4,49],[10,49],[10,49],[25,49],[0,1]],\"A\":[2,3],\"B\":[4]}。請依 [P_A,P_B,P_intersection,product,independent,conditional_defined,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)","explanation_zh":"Wave4根節點核對=(5/7, 0, 0, 0, 是, 否, conditional_probability_undefined_use_product_definition)；依完整明示資料重算；完整有限／精確座標切片不自動升格為任意無限定理；主資格是P(A交B)=P(A)P(B)；條件式只在正分母使用且pairwise不冒充mutual。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["事件獨立"]},"variant":{"family_id":"qf-mod27-eventind-zero-probability-boundary","seed":202610276100,"parameters":{"masses":[[4,49],[10,49],[10,49],[25,49],[0,1]],"A":[2,3],"B":[4],"domain":"Exact_finite_event_independence","operation":"eventind-zero-probability-boundary","semantic_template":"qf-mod27-eventind-zero-probability-boundary/{\"A\":[2,3],\"B\":[4],\"masses\":[[4,49],[10,49],[10,49],[25,49],[0,1]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般完備性、內積／有界性、mutual independence、directed graph、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}