{ "schema_version": "ocme-reviewed-question-reader-v1", "question_id": "q-20260914-finite-sample-space-completeness-0009", "pilot_number": "R0070-35584", "number": 35584, "family_id": "qf-finite-sample-space-completeness", "title": { "zh-Hant": "第 35584 題：有限樣本空間完整性", "en": "Question 35584: Completeness of a Finite Sample Space" }, "original_question": { "schema_version": "ocme-question-v0.1", "id": "q-20260914-finite-sample-space-completeness-0009", "batch_id": "batch-20260914-domain-foundations", "language": "zh-Hant", "source_mko_ids": [ "mko-sample-space" ], "title_zh": "有限樣本空間完整性", "stem_zh": "試驗為「一次讀取明示標記卡 標記81、標記82」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記81、標記82}。候選 S={標記81、標記82、非此試驗結果9} 是否完整？", "answer": { "kind": "choice", "value": "否", "choices": [ "是", "否" ], "explanation_zh": "列入「非此試驗結果9」但它不在本題明示的基本結果中，因此列舉不完整；本題不從樣本空間推論機率。" }, "difficulty": { "band": "undergraduate_core", "level": 3, "skills": [ "樣本空間", "有限列舉" ] }, "variant": { "family_id": "qf-finite-sample-space-completeness", "seed": 20260962, "parameters": { "experiment": "一次讀取明示標記卡 標記81、標記82", "observation_scale": "一次明示有限試驗", "expected_outcomes": [ "標記81", "標記82" ], "listed_outcomes": [ "標記81", "標記82", "非此試驗結果9" ], "mode": "extra_outcome", "semantic_template": "qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記81\",\"標記82\"],\"experiment\":\"一次讀取明示標記卡 標記81、標記82\",\"listed_outcomes\":[\"標記81\",\"標記82\",\"非此試驗結果9\"],\"mode\":\"extra_outcome\",\"observation_scale\":\"一次明示有限試驗\"}" } }, "verification": { "status": "candidate", "checks": [ "schema_pending", "independent_recomputation_pending" ], "warning_zh": "本題僅依明示的有限參數重算或分類；不構成普遍證明、形式 Evidence、人工審查或發布。" }, "provenance": { "generator_role": "question_producer", "generator_model": "GPT-5.6 Terra", "generated_at": "2026-09-14", "contract_version": "ocme-question-factory-v0.1" } }, "original_english_edition": { "schema_version": "ocme-question-localization-v0.1", "question_id": "q-20260914-finite-sample-space-completeness-0009", "batch_id": "batch-20260914-domain-foundations", "locale": "en", "translation_state": "ai_candidate", "source": { "question_sha256": "346b46d4bc343e81a8e99e87487ffd4637a5d0dee72dbecf9ebb8222ec29a7b3", "family_id": "qf-finite-sample-space-completeness", "seed": 20260962, "semantic_template": "qf-finite-sample-space-completeness/{\"expected_outcomes\":[\"標記81\",\"標記82\"],\"experiment\":\"一次讀取明示標記卡 標記81、標記82\",\"listed_outcomes\":[\"標記81\",\"標記82\",\"非此試驗結果9\"],\"mode\":\"extra_outcome\",\"observation_scale\":\"一次明示有限試驗\"}" }, "fields": { "title": "Completeness of a Finite Sample Space", "stem": "The experiment is one draw from explicitly labelled cards with elementary outcomes label 81, label 82. At this observation scale the candidate sample space is S={label 81, label 82, outcome outside this experiment 9}. Is it complete?", "answer": { "kind": "choice", "value": "No", "choices": [ "Yes", "No" ], "explanation": "The candidate includes an outcome outside the explicitly stated experiment, so it is not the exact sample space." }, "skills": [ "sample spaces", "finite enumeration" ], "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review." } }, "givens": [ { "id": "G001", "text": { "zh-Hant": "試驗為「一次讀取明示標記卡 標記81、標記82」，觀察尺度是一次明示有限試驗；所有基本結果應為 {標記81、標記82}。候選 S={標記81、標記82、非此試驗結果9} 是否完整？", "en": "The experiment is one draw from explicitly labelled cards with elementary outcomes label 81, label 82. At this observation scale the candidate sample space is S={label 81, label 82, outcome outside this experiment 9}. Is it complete?" } } ], "steps": [ { "id": "S001", "uses": [ "G001" ], "before": "source roles = [qf-finite-sample-space-completeness, [expected_outcomes, experiment, listed_outcomes, mode, observation_scale]]", "after": "derived = [sample, null, null]", "relation": "implies", "rule_id": "R70_SOURCE_bank_specific_interface", "conditions": [], "explanation": { "zh-Hant": "只使用此bank真正明示的欄位、operation/domain與型別；BASE容許保留額外metadata，不把LDL SAFE/集合上限或其他bank的去重規則搬來。", "en": "Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S002", "uses": [ "G001", "S001" ], "before": "source roles = [一次讀取明示標記卡 標記81、標記82, 一次明示有限試驗, [標記81, 標記82], [標記81, 標記82, 非此試驗結果9]]", "after": "derived = [completeness only]", "relation": "implies", "rule_id": "Sample_GIVEN_complete_elementary_outcomes_at_declared_scale", "conditions": [], "explanation": { "zh-Hant": "題目已在指定觀察尺度明示完整基本結果清單A，核B是否恰好A；不是從局部觀測猜宇宙，也不賦予等可能或機率。", "en": "A is GIVEN as the COMPLETE elementary-outcome list at the declared observation scale.Check whether B is exactly A;do not infer the universe from partial observations or assign equal likelihood/probabilities." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S003", "uses": [ "G001", "S002" ], "before": "source roles = [標記81, [標記81, 標記82, 非此試驗結果9]]", "after": "derived = [是]", "relation": "implies", "rule_id": "Sample_EACH_expected_outcome_is_listed", "conditions": [], "explanation": { "zh-Hant": "逐應有結果檢查是否列入，不因列出的都合法就忽略漏項。", "en": "Check EACH required outcome for inclusion;all listed outcomes being legal does not rule out a missing one." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S004", "uses": [ "G001", "S003" ], "before": "source roles = [標記82, [標記81, 標記82, 非此試驗結果9]]", "after": "derived = [是]", "relation": "implies", "rule_id": "Sample_EACH_expected_outcome_is_listed", "conditions": [], "explanation": { "zh-Hant": "逐應有結果檢查是否列入，不因列出的都合法就忽略漏項。", "en": "Check EACH required outcome for inclusion;all listed outcomes being legal does not rule out a missing one." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S005", "uses": [ "G001", "S004" ], "before": "source roles = [標記81, [標記81, 標記82]]", "after": "derived = [是]", "relation": "implies", "rule_id": "Sample_EACH_listed_outcome_is_possible", "conditions": [], "explanation": { "zh-Hant": "逐已列結果檢查是否真在明示全集；沒有漏項仍可能多列不可能結果。", "en": "Check EACH listed outcome against the GIVEN universe;absence of omissions does not rule out impossible extras." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S006", "uses": [ "G001", "S005" ], "before": "source roles = [標記82, [標記81, 標記82]]", "after": "derived = [是]", "relation": "implies", "rule_id": "Sample_EACH_listed_outcome_is_possible", "conditions": [], "explanation": { "zh-Hant": "逐已列結果檢查是否真在明示全集；沒有漏項仍可能多列不可能結果。", "en": "Check EACH listed outcome against the GIVEN universe;absence of omissions does not rule out impossible extras." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S007", "uses": [ "G001", "S006" ], "before": "source roles = [非此試驗結果9, [標記81, 標記82]]", "after": "derived = [否]", "relation": "implies", "rule_id": "Sample_EACH_listed_outcome_is_possible", "conditions": [], "explanation": { "zh-Hant": "逐已列結果檢查是否真在明示全集；沒有漏項仍可能多列不可能結果。", "en": "Check EACH listed outcome against the GIVEN universe;absence of omissions does not rule out impossible extras." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null }, { "id": "S008", "uses": [ "G001", "S007" ], "before": "source roles = [[], [非此試驗結果9], extra_outcome]", "after": "derived = [否]", "relation": "implies", "rule_id": "Sample_BOTH_inclusions_and_postderived_mode", "conditions": [], "explanation": { "zh-Hant": "兩方向都過才完整；若同時漏與多列仍No，mode依原契約先記漏項。mode只在集合比較後核對。", "en": "Completeness requires BOTH inclusions.If both omissions and extras occur,the answer remains No;the source mode prioritizes omissions.Check mode only AFTER set comparison." }, "reverse_audit": { "kind": "premise_and_result_audit", "explanation": { "zh-Hant": "反查本題原始操作數、角色與必要條件；重建下一步，不把單向推論倒當等價。數值/有限表核對不是任意命題的形式證明。原題、中英來源、MKO、AST、狀態與歷史均保留。", "en": "Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved." } }, "arithmetic": null } ], "math_model": { "result": "否" }, "conclusion": { "canonical_value": "否", "explanation": { "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。", "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged." } }, "definition_note": { "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。", "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate." }, "source": { "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db", "question_binding": { "batch_id": "batch-20260914-domain-foundations", "batch_path": "public/data/questions/batches/batch-20260914-domain-foundations/questions.jsonl", "batch_sha256": "726b3f94ccd05d8c91cc7e306b42fd71b6d9040e194db91739a250d488fd1de7", "original_line": 49, "original_line_sha256": "b300f2c31c69539f761ec45b23f2c6e9b49c59c8f6662f9ffdb8ab41ea340492", "question_compact_sha256": "346b46d4bc343e81a8e99e87487ffd4637a5d0dee72dbecf9ebb8222ec29a7b3", "english_row_compact_sha256": "08cc12fc7a62a87460cdc83628f9320e7c6ed9d8ff83de5d3fa780e0f19a94c6", "english_manifest_path": "public/data/i18n/editions/batch-20260914-domain-foundations.en.json", "english_rows_path": "public/data/i18n/questions/batch-20260914-domain-foundations.en.jsonl" }, "mko_bindings": { "mko-sample-space": { "sha256": "c58b0d07252ece257a4143fd10f0f25b249023f4ed50bc6d393f4752a91267f7", "english_sha256": "ba452c266ef8c6ab4b549a3ccb6bc04a19fc7fafef1934d17f821c9ef4c04756", "original_path": "public/data/mko/sample-space.json", "english_path": "public/data/i18n/editions/mko-sample-space.en.json" } }, "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff", "selected_part_sha256": "20c37a7e64ee5969e7606c5cc3a00e575002ebebdfe82873521cc3d7c608caff", "original_candidate_sha256": "ae2fc1f83846062e9d123e3cbbfae9f30458edbb2e5dfef80ef98dd72b7c28d9", "original_candidate_line_sha256": "ae2fc1f83846062e9d123e3cbbfae9f30458edbb2e5dfef80ef98dd72b7c28d9" }, "historical_source_state": { "review_state": { "derivation": "candidate_authored_and_locally_checked", "source_question_state": "candidate", "independent_AI_or_human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN" }, "scope_note": { "zh-Hant": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。", "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human review or general formal proof.Original questions,answers,MKOs,formulas,ASTs and history remain unchanged." }, "label": "Frozen producer metadata; current per-question review is separate below." }, "revision": { "id": "review-20261026-012-p71", "review_date": "2026-10-26", "owner_authorized_reader_publication": true, "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.", "review_receipts": { "semantic_review_sha256": "9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80", "question_first_witness_sha256": "c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab" }, "status": "second_context_reviewed", "mathematical_semantics": true, "bilingual_semantics": true, "steps_reviewed": 8, "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction", "exact_question_first_check": { "model_sha256": "bca71e82a3b603522a7c8b63fcbc81f6ac763288e5b122c1663da40e54865d65", "arithmetic_steps": 0 }, "uses_answer_as_premise": false, "human_review": "NOT_PERFORMED", "formalization": "not_formalized", "Lean": "NOT_RUN", "Canonical_truth_promotion": false, "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged." } }