{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0001","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"65c29b248dbe9d0c71e8e4c7195c9a2f4c62cec1a7941d9bce2874346025ce44","family_id":"qf-finite-event-subset-validity","seed":20260919,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[2,9],\"F\":\"P(S)\",\"S\":[1,2,3]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={1, 2, 3}, with F=P(S) explicitly selected. Is E={2, 9} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"9 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0002","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"41369eaf20f01c528afda042df903747ed5b6594312f2adb6a333235af3f2796","family_id":"qf-finite-event-subset-validity","seed":20260920,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[5,7],\"F\":\"P(S)\",\"S\":[5,6,7]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={5, 6, 7}, with F=P(S) explicitly selected. Is E={5, 7} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0003","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5eab4cd58082388caebb7390a18e3445a587096c213f6274597f3093512bf6f2","family_id":"qf-finite-event-subset-validity","seed":20260921,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[10,17],\"F\":\"P(S)\",\"S\":[9,10,11]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={9, 10, 11}, with F=P(S) explicitly selected. Is E={10, 17} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"17 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0004","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7d9a6dfd55f5bd9fe258b2f63e299377372c26e75345be0bfefd929099d3f6a9","family_id":"qf-finite-event-subset-validity","seed":20260922,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[13,15],\"F\":\"P(S)\",\"S\":[13,14,15]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={13, 14, 15}, with F=P(S) explicitly selected. Is E={13, 15} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0005","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e3f4bd8c32bf171d299c6d728bec872f6ef455962442cbe33e6f62a098577fa7","family_id":"qf-finite-event-subset-validity","seed":20260923,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[18,25],\"F\":\"P(S)\",\"S\":[17,18,19]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={17, 18, 19}, with F=P(S) explicitly selected. Is E={18, 25} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"25 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0006","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c4b25123c30b43dc3c1d0248998f77dcc8afbf291c3342837c0c4856ce0fd8b","family_id":"qf-finite-event-subset-validity","seed":20260924,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[21,23],\"F\":\"P(S)\",\"S\":[21,22,23]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={21, 22, 23}, with F=P(S) explicitly selected. Is E={21, 23} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0007","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3fbef87969f701ff9552f66d420e6754fbf8a7a0d261b246282cb3f42fa41714","family_id":"qf-finite-event-subset-validity","seed":20260925,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[26,33],\"F\":\"P(S)\",\"S\":[25,26,27]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={25, 26, 27}, with F=P(S) explicitly selected. Is E={26, 33} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"33 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0008","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"2d3fdced8a32abbdab74fd060fa02682be2818df26118b82120f2adae45a142d","family_id":"qf-finite-event-subset-validity","seed":20260926,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[29,31],\"F\":\"P(S)\",\"S\":[29,30,31]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={29, 30, 31}, with F=P(S) explicitly selected. Is E={29, 31} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0009","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"db4a91cf06fe622f5a55f07709433e8fb035a4df6365e193894b28bb585064bd","family_id":"qf-finite-event-subset-validity","seed":20260927,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[34,41],\"F\":\"P(S)\",\"S\":[33,34,35]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={33, 34, 35}, with F=P(S) explicitly selected. Is E={34, 41} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"41 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0010","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c9ed2f745432cf57756e534cd30e52a499b47b60a1e846f139222b8539366de8","family_id":"qf-finite-event-subset-validity","seed":20260928,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[37,39],\"F\":\"P(S)\",\"S\":[37,38,39]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={37, 38, 39}, with F=P(S) explicitly selected. Is E={37, 39} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0011","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1936ca47178fd2cc56d2d87e919ed82ddc1cad7cbd7b53af22857058030b26e8","family_id":"qf-finite-event-subset-validity","seed":20260929,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[42,49],\"F\":\"P(S)\",\"S\":[41,42,43]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={41, 42, 43}, with F=P(S) explicitly selected. Is E={42, 49} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"49 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0012","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5a541abd3b3eddbad1f74aeb06c74718f3389cf5b815677e2f1ad0e77ff49d16","family_id":"qf-finite-event-subset-validity","seed":20260930,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[45,47],\"F\":\"P(S)\",\"S\":[45,46,47]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={45, 46, 47}, with F=P(S) explicitly selected. Is E={45, 47} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0013","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c6225e4d16b0ed233cb52da4f46060bb97db53ed8fdf34708ea2931b0ac9c3f8","family_id":"qf-finite-event-subset-validity","seed":20260931,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[50,57],\"F\":\"P(S)\",\"S\":[49,50,51]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={49, 50, 51}, with F=P(S) explicitly selected. Is E={50, 57} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"57 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0014","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fc7df9fb70df6d82e7b81c172164475b79387acce59fdf268a2ce9d68cd1bc3e","family_id":"qf-finite-event-subset-validity","seed":20260932,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[53,55],\"F\":\"P(S)\",\"S\":[53,54,55]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={53, 54, 55}, with F=P(S) explicitly selected. Is E={53, 55} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0015","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"874712fd1a277ae213a7b06c57d1c7e2402cb479dafc2ff96f214201416ad86b","family_id":"qf-finite-event-subset-validity","seed":20260933,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[58,65],\"F\":\"P(S)\",\"S\":[57,58,59]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={57, 58, 59}, with F=P(S) explicitly selected. Is E={58, 65} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"65 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0016","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55eafb27b65e2baac8dc863ce5762595aa093ed220ad39f160d93fbb6dc4d33f","family_id":"qf-finite-event-subset-validity","seed":20260934,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[61,63],\"F\":\"P(S)\",\"S\":[61,62,63]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={61, 62, 63}, with F=P(S) explicitly selected. Is E={61, 63} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0017","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d50c5136d86a81cc568d7e277240bf98434602f2d034c4e743ff3cb461aea4fb","family_id":"qf-finite-event-subset-validity","seed":20260935,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[66,73],\"F\":\"P(S)\",\"S\":[65,66,67]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={65, 66, 67}, with F=P(S) explicitly selected. Is E={66, 73} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"73 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0018","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a10cb8ba5a00bddb2d9c3e16790d2272404f08fef9cc4bd147ab49e5a78f417d","family_id":"qf-finite-event-subset-validity","seed":20260936,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[69,71],\"F\":\"P(S)\",\"S\":[69,70,71]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={69, 70, 71}, with F=P(S) explicitly selected. Is E={69, 71} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0019","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"55860d50f18559e47b913cea205ac56b00a85a7dbf2e083b2e889f63b967eb8e","family_id":"qf-finite-event-subset-validity","seed":20260937,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[74,81],\"F\":\"P(S)\",\"S\":[73,74,75]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={73, 74, 75}, with F=P(S) explicitly selected. Is E={74, 81} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"81 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0020","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1e8e67d683145bc511ba0f0cb3d6be9a9bd366c67afec086e245290ff82771b9","family_id":"qf-finite-event-subset-validity","seed":20260938,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[77,79],\"F\":\"P(S)\",\"S\":[77,78,79]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={77, 78, 79}, with F=P(S) explicitly selected. Is E={77, 79} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0021","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7f12bc48eaacc162d4fc910e3d2c86f51f48eda192ddc334cc3262509ecf34a3","family_id":"qf-finite-event-subset-validity","seed":20260939,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[82,89],\"F\":\"P(S)\",\"S\":[81,82,83]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={81, 82, 83}, with F=P(S) explicitly selected. Is E={82, 89} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"89 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0022","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"091b8aa64be0fb6a4103b214ca866d4117b299b8d7a38656b3d9a270865cd80a","family_id":"qf-finite-event-subset-validity","seed":20260940,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[85,87],\"F\":\"P(S)\",\"S\":[85,86,87]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={85, 86, 87}, with F=P(S) explicitly selected. Is E={85, 87} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0023","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f80c1693ffbbae0186a1a4360e6f7e4ca7232459f086d69f4880d5607b5f51f5","family_id":"qf-finite-event-subset-validity","seed":20260941,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[90,97],\"F\":\"P(S)\",\"S\":[89,90,91]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={89, 90, 91}, with F=P(S) explicitly selected. Is E={90, 97} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"97 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0024","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"722e16492669cc45ddf808515dd5411c21aec484d6eae38fa29c32da680beacb","family_id":"qf-finite-event-subset-validity","seed":20260942,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[93,95],\"F\":\"P(S)\",\"S\":[93,94,95]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={93, 94, 95}, with F=P(S) explicitly selected. Is E={93, 95} an event in this model?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"Every element of E belongs to S, so E is a subset of S and therefore an event in F=P(S)."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-subset-validity-0025","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4b3d0753364ceb0b062594789f71393f26e00611a41cf011a6302f2349453930","family_id":"qf-finite-event-subset-validity","seed":20260943,"semantic_template":"qf-finite-event-subset-validity/{\"E\":[98,105],\"F\":\"P(S)\",\"S\":[97,98,99]}"},"fields":{"title":"Event Validity in a Finite Powerset Model","stem":"Let S={97, 98, 99}, with F=P(S) explicitly selected. Is E={98, 105} an event in this model?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"105 is not in S, so E is not a subset of S."},"skills":["events","powerset model"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0001","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9c7c10c2eb5bc44eb6e4efbe96b6bdc250628a392bb6049b810498c9420fde97","family_id":"qf-outcome-versus-event-role","seed":20261019,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[1],\"F\":\"P(S)\",\"S\":[1,2,3],\"x\":1}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={1, 2, 3} and F=P(S). 1 is a single outcome, while {1} is an event. Is the role of 1 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"1 is an element of S; {1} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0002","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"038be5941be809aadf9683e7eec9b2a0958a1685a0e9734609663e52a8518466","family_id":"qf-outcome-versus-event-role","seed":20261020,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[6],\"F\":\"P(S)\",\"S\":[5,6,7],\"x\":6}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={5, 6, 7} and F=P(S). 6 is a single outcome, while {6} is an event. Is the role of 6 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"6 is an element of S; {6} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0003","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"614186ef4bea64693b73c712dbf3c684a5db727d444f2a4dfd9fc03edf87dd6d","family_id":"qf-outcome-versus-event-role","seed":20261021,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[11],\"F\":\"P(S)\",\"S\":[9,10,11],\"x\":11}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={9, 10, 11} and F=P(S). 11 is a single outcome, while {11} is an event. Is the role of 11 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"11 is an element of S; {11} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0004","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"3aa800aa34651ab67e63e3cb25ad940d383772f73de8f33f3ce31f7bb0f86965","family_id":"qf-outcome-versus-event-role","seed":20261022,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[13],\"F\":\"P(S)\",\"S\":[13,14,15],\"x\":13}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={13, 14, 15} and F=P(S). 13 is a single outcome, while {13} is an event. Is the role of 13 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"13 is an element of S; {13} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0005","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"03060d24da769ac87e3f2ab1a9a80fc583e75ed907f227f8073456cd2e59fa93","family_id":"qf-outcome-versus-event-role","seed":20261023,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[18],\"F\":\"P(S)\",\"S\":[17,18,19],\"x\":18}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={17, 18, 19} and F=P(S). 18 is a single outcome, while {18} is an event. Is the role of 18 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"18 is an element of S; {18} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0006","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ac6b7af940ab2a33a4bf9adb460330edfe07334ab210d0cf2e650d18d4ddaf12","family_id":"qf-outcome-versus-event-role","seed":20261024,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[23],\"F\":\"P(S)\",\"S\":[21,22,23],\"x\":23}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={21, 22, 23} and F=P(S). 23 is a single outcome, while {23} is an event. Is the role of 23 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"23 is an element of S; {23} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0007","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"624d63268ecef995a3f3acece0abaeb5d426c09efbf9ebbb6a662956b88d1185","family_id":"qf-outcome-versus-event-role","seed":20261025,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[25],\"F\":\"P(S)\",\"S\":[25,26,27],\"x\":25}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={25, 26, 27} and F=P(S). 25 is a single outcome, while {25} is an event. Is the role of 25 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"25 is an element of S; {25} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0008","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"4a7f65d58dc5ac26f357518b409f39ee1a98de2ec9fd90cb48b771062f69176f","family_id":"qf-outcome-versus-event-role","seed":20261026,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[30],\"F\":\"P(S)\",\"S\":[29,30,31],\"x\":30}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={29, 30, 31} and F=P(S). 30 is a single outcome, while {30} is an event. Is the role of 30 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"30 is an element of S; {30} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0009","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9131ecc6a9337f847e52436072487f430ae9051b25bf7e49a73b95ef9957b2c","family_id":"qf-outcome-versus-event-role","seed":20261027,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[35],\"F\":\"P(S)\",\"S\":[33,34,35],\"x\":35}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={33, 34, 35} and F=P(S). 35 is a single outcome, while {35} is an event. Is the role of 35 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"35 is an element of S; {35} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0010","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7b26c1600765b18bb8936ca4d2be8010f296e3e23d3a860209c64f06c39a5074","family_id":"qf-outcome-versus-event-role","seed":20261028,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[37],\"F\":\"P(S)\",\"S\":[37,38,39],\"x\":37}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={37, 38, 39} and F=P(S). 37 is a single outcome, while {37} is an event. Is the role of 37 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"37 is an element of S; {37} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0011","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7c44deba0635d94194578f10c3e2af1b1adbc3aa3c4fba46283391fa2344f143","family_id":"qf-outcome-versus-event-role","seed":20261029,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[42],\"F\":\"P(S)\",\"S\":[41,42,43],\"x\":42}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={41, 42, 43} and F=P(S). 42 is a single outcome, while {42} is an event. Is the role of 42 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"42 is an element of S; {42} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0012","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"9e7d950be67449601cc367d0c6041531f9e626c45de0307731dc23e0a98256da","family_id":"qf-outcome-versus-event-role","seed":20261030,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[47],\"F\":\"P(S)\",\"S\":[45,46,47],\"x\":47}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={45, 46, 47} and F=P(S). 47 is a single outcome, while {47} is an event. Is the role of 47 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"47 is an element of S; {47} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0013","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"665379f5336aba26db26ed8ec0063fc6aa13d87cfa6a8225e9071b794251dbc5","family_id":"qf-outcome-versus-event-role","seed":20261031,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[49],\"F\":\"P(S)\",\"S\":[49,50,51],\"x\":49}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={49, 50, 51} and F=P(S). 49 is a single outcome, while {49} is an event. Is the role of 49 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"49 is an element of S; {49} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0014","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"47e465fcf931d63f79de775da3675f4078c709f9b319df96028b7cc3ff799c8a","family_id":"qf-outcome-versus-event-role","seed":20261032,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[54],\"F\":\"P(S)\",\"S\":[53,54,55],\"x\":54}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={53, 54, 55} and F=P(S). 54 is a single outcome, while {54} is an event. Is the role of 54 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"54 is an element of S; {54} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0015","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"45320a619bcb9c856862b8bcc0139b7daa19c7d98006cccb6c5d8d3da3651b54","family_id":"qf-outcome-versus-event-role","seed":20261033,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[59],\"F\":\"P(S)\",\"S\":[57,58,59],\"x\":59}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={57, 58, 59} and F=P(S). 59 is a single outcome, while {59} is an event. Is the role of 59 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"59 is an element of S; {59} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0016","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0fc4b33318ed5cbb5f3b20cfdbd582a5ba0d9855b2a3593cb063aa3f4f87d12b","family_id":"qf-outcome-versus-event-role","seed":20261034,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[61],\"F\":\"P(S)\",\"S\":[61,62,63],\"x\":61}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={61, 62, 63} and F=P(S). 61 is a single outcome, while {61} is an event. Is the role of 61 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"61 is an element of S; {61} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0017","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e091528aa3f16e56d216873e3a573a6839f992549c61550165a058a69161a28c","family_id":"qf-outcome-versus-event-role","seed":20261035,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[66],\"F\":\"P(S)\",\"S\":[65,66,67],\"x\":66}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={65, 66, 67} and F=P(S). 66 is a single outcome, while {66} is an event. Is the role of 66 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"66 is an element of S; {66} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0018","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"61f5b4698e9ae104aeae683fe4c70243f9928e682339bb0fc5d12539a2dd616f","family_id":"qf-outcome-versus-event-role","seed":20261036,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[71],\"F\":\"P(S)\",\"S\":[69,70,71],\"x\":71}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={69, 70, 71} and F=P(S). 71 is a single outcome, while {71} is an event. Is the role of 71 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"71 is an element of S; {71} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0019","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ea405203b419d1c7d1e201e74fbe3e949902d39712908ea538f103515a162d2f","family_id":"qf-outcome-versus-event-role","seed":20261037,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[73],\"F\":\"P(S)\",\"S\":[73,74,75],\"x\":73}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={73, 74, 75} and F=P(S). 73 is a single outcome, while {73} is an event. Is the role of 73 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"73 is an element of S; {73} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0020","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b439ace95ceecc57e88ba625b17eec950fb14bcb57c8cce7ef46f4bfa9dc9211","family_id":"qf-outcome-versus-event-role","seed":20261038,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[78],\"F\":\"P(S)\",\"S\":[77,78,79],\"x\":78}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={77, 78, 79} and F=P(S). 78 is a single outcome, while {78} is an event. Is the role of 78 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"78 is an element of S; {78} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0021","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"36536348f1be372c56747db6b44b5f399b981b9ef5067bbc242c794710d0ad6d","family_id":"qf-outcome-versus-event-role","seed":20261039,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[83],\"F\":\"P(S)\",\"S\":[81,82,83],\"x\":83}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={81, 82, 83} and F=P(S). 83 is a single outcome, while {83} is an event. Is the role of 83 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"83 is an element of S; {83} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0022","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cbe1cfe0b61f9fa704bbb3f7277b3ff19d45c92701ae8290c52ee97475e4b485","family_id":"qf-outcome-versus-event-role","seed":20261040,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[85],\"F\":\"P(S)\",\"S\":[85,86,87],\"x\":85}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={85, 86, 87} and F=P(S). 85 is a single outcome, while {85} is an event. Is the role of 85 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"85 is an element of S; {85} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0023","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"824fd5e576acb72efd37de6f14c3fa63d6139391259105bf235448283710b6e1","family_id":"qf-outcome-versus-event-role","seed":20261041,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[90],\"F\":\"P(S)\",\"S\":[89,90,91],\"x\":90}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={89, 90, 91} and F=P(S). 90 is a single outcome, while {90} is an event. Is the role of 90 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"90 is an element of S; {90} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0024","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"75aade1e8025222fd7f83bbbadb13a871a5c5196dcb9cce705492dac032c41df","family_id":"qf-outcome-versus-event-role","seed":20261042,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[95],\"F\":\"P(S)\",\"S\":[93,94,95],\"x\":95}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={93, 94, 95} and F=P(S). 95 is a single outcome, while {95} is an event. Is the role of 95 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"95 is an element of S; {95} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-outcome-versus-event-role-0025","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b058888933432cea409b59eb1327c33c80c44c41712b7f684d4e15a42122e7a0","family_id":"qf-outcome-versus-event-role","seed":20261043,"semantic_template":"qf-outcome-versus-event-role/{\"E\":[97],\"F\":\"P(S)\",\"S\":[97,98,99],\"x\":97}"},"fields":{"title":"Outcome Versus Event","stem":"Let S={97, 98, 99} and F=P(S). 97 is a single outcome, while {97} is an event. Is the role of 97 “event set”?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"97 is an element of S; {97} is the event written as a set of outcomes."},"skills":["outcomes and events"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0001","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"12e1bb616b274c45ccc4f0c3252ce054d1fc79dc950a3e15aa130ba495c22081","family_id":"qf-finite-event-occurrence","seed":20261119,"semantic_template":"qf-finite-event-occurrence/{\"E\":[2],\"F\":\"P(S)\",\"S\":[1,2,3],\"x\":1}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={1, 2, 3}, F=P(S), and E={2}. The observed outcome is 1. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"1 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0002","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d858d310967a9e7af7aa213dcada929c96c8afceec88ed030375054af08eed83","family_id":"qf-finite-event-occurrence","seed":20261120,"semantic_template":"qf-finite-event-occurrence/{\"E\":[5,7],\"F\":\"P(S)\",\"S\":[5,6,7],\"x\":5}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={5, 6, 7}, F=P(S), and E={5, 7}. The observed outcome is 5. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"5 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0003","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed6279ec8f9150c7ed14464a066de2596bd80af58a9d12a3730c1d58ca31c628","family_id":"qf-finite-event-occurrence","seed":20261121,"semantic_template":"qf-finite-event-occurrence/{\"E\":[10],\"F\":\"P(S)\",\"S\":[9,10,11],\"x\":9}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={9, 10, 11}, F=P(S), and E={10}. The observed outcome is 9. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"9 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0004","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e1c82fe2c8e2c0db7dd792e31c5d844bbd2dc21ae2a6313e65a037cea840d053","family_id":"qf-finite-event-occurrence","seed":20261122,"semantic_template":"qf-finite-event-occurrence/{\"E\":[13,15],\"F\":\"P(S)\",\"S\":[13,14,15],\"x\":13}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={13, 14, 15}, F=P(S), and E={13, 15}. The observed outcome is 13. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"13 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0005","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"34fc2a237fb886c3d0c391d8a02d2e165bed22d5e9c2692849b7f5c6fd6668a0","family_id":"qf-finite-event-occurrence","seed":20261123,"semantic_template":"qf-finite-event-occurrence/{\"E\":[18],\"F\":\"P(S)\",\"S\":[17,18,19],\"x\":17}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={17, 18, 19}, F=P(S), and E={18}. The observed outcome is 17. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"17 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0006","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1a0f7ee0bfc2d58265f65937f14118764fb76b633d342d1dec6109299db3613a","family_id":"qf-finite-event-occurrence","seed":20261124,"semantic_template":"qf-finite-event-occurrence/{\"E\":[21,23],\"F\":\"P(S)\",\"S\":[21,22,23],\"x\":21}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={21, 22, 23}, F=P(S), and E={21, 23}. The observed outcome is 21. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"21 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0007","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"b88a406ca0365cb3f7614386e55ba949c95a0553d726907ec0af0cc7b78a32a0","family_id":"qf-finite-event-occurrence","seed":20261125,"semantic_template":"qf-finite-event-occurrence/{\"E\":[26],\"F\":\"P(S)\",\"S\":[25,26,27],\"x\":25}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={25, 26, 27}, F=P(S), and E={26}. The observed outcome is 25. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"25 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0008","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6115dce104fe71203aa5d86edcf8ec14fdc4a1ca19d4bd84e9620dc9d9cfd539","family_id":"qf-finite-event-occurrence","seed":20261126,"semantic_template":"qf-finite-event-occurrence/{\"E\":[29,31],\"F\":\"P(S)\",\"S\":[29,30,31],\"x\":29}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={29, 30, 31}, F=P(S), and E={29, 31}. The observed outcome is 29. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"29 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0009","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0aac016bfe0746de44e115b907a850f13cbded746455419356f432a1aa260707","family_id":"qf-finite-event-occurrence","seed":20261127,"semantic_template":"qf-finite-event-occurrence/{\"E\":[34],\"F\":\"P(S)\",\"S\":[33,34,35],\"x\":33}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={33, 34, 35}, F=P(S), and E={34}. The observed outcome is 33. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"33 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0010","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"56d72a32e065ba312429c4c10428af16d87455cf8ad89fffcdd5d28ccd33f226","family_id":"qf-finite-event-occurrence","seed":20261128,"semantic_template":"qf-finite-event-occurrence/{\"E\":[37,39],\"F\":\"P(S)\",\"S\":[37,38,39],\"x\":37}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={37, 38, 39}, F=P(S), and E={37, 39}. The observed outcome is 37. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"37 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0011","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e065a0264940256ce286497f61629781f78880eea9a7ca563fcc6083d9d2a9b9","family_id":"qf-finite-event-occurrence","seed":20261129,"semantic_template":"qf-finite-event-occurrence/{\"E\":[42],\"F\":\"P(S)\",\"S\":[41,42,43],\"x\":41}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={41, 42, 43}, F=P(S), and E={42}. The observed outcome is 41. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"41 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0012","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ced9502dff4626be6e77ee14aefae9fea743696a7ec0a54d0167a7de16a1eeab","family_id":"qf-finite-event-occurrence","seed":20261130,"semantic_template":"qf-finite-event-occurrence/{\"E\":[45,47],\"F\":\"P(S)\",\"S\":[45,46,47],\"x\":45}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={45, 46, 47}, F=P(S), and E={45, 47}. The observed outcome is 45. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"45 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0013","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e4c30334b362f838a95ed7c328e765030b8ba82cb1352750f3c04987df93a0e7","family_id":"qf-finite-event-occurrence","seed":20261131,"semantic_template":"qf-finite-event-occurrence/{\"E\":[50],\"F\":\"P(S)\",\"S\":[49,50,51],\"x\":49}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={49, 50, 51}, F=P(S), and E={50}. The observed outcome is 49. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"49 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0014","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"fd591471c23290f2afad3b91603ddf43b6dacd00fe4fac3d3d0b7198753c7327","family_id":"qf-finite-event-occurrence","seed":20261132,"semantic_template":"qf-finite-event-occurrence/{\"E\":[53,55],\"F\":\"P(S)\",\"S\":[53,54,55],\"x\":53}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={53, 54, 55}, F=P(S), and E={53, 55}. The observed outcome is 53. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"53 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0015","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"c379ee53be734e2be95c09d766da51d434d2c9705e35374a338c51f342eaa0aa","family_id":"qf-finite-event-occurrence","seed":20261133,"semantic_template":"qf-finite-event-occurrence/{\"E\":[58],\"F\":\"P(S)\",\"S\":[57,58,59],\"x\":57}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={57, 58, 59}, F=P(S), and E={58}. The observed outcome is 57. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"57 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0016","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1f83a54781b1873caf4cc6615dfe02f4aec027ee4d47af22a72c851986ee0aff","family_id":"qf-finite-event-occurrence","seed":20261134,"semantic_template":"qf-finite-event-occurrence/{\"E\":[61,63],\"F\":\"P(S)\",\"S\":[61,62,63],\"x\":61}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={61, 62, 63}, F=P(S), and E={61, 63}. The observed outcome is 61. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"61 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0017","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6e789f37f9105f532d78622c1d7f11c9fade4648a0248b04376301f854fc1fac","family_id":"qf-finite-event-occurrence","seed":20261135,"semantic_template":"qf-finite-event-occurrence/{\"E\":[66],\"F\":\"P(S)\",\"S\":[65,66,67],\"x\":65}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={65, 66, 67}, F=P(S), and E={66}. The observed outcome is 65. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"65 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0018","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"34d20c797e7a1bf01b1a18e3d1e93a2764d7b7bd92ef141418ad732d2f777359","family_id":"qf-finite-event-occurrence","seed":20261136,"semantic_template":"qf-finite-event-occurrence/{\"E\":[69,71],\"F\":\"P(S)\",\"S\":[69,70,71],\"x\":69}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={69, 70, 71}, F=P(S), and E={69, 71}. The observed outcome is 69. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"69 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0019","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"044e106f2dc5dd6274be919920176dc7d89577f8a6734c274fbe7a0579f1f508","family_id":"qf-finite-event-occurrence","seed":20261137,"semantic_template":"qf-finite-event-occurrence/{\"E\":[74],\"F\":\"P(S)\",\"S\":[73,74,75],\"x\":73}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={73, 74, 75}, F=P(S), and E={74}. The observed outcome is 73. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"73 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0020","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1fe647dd1d26019554314e4f8274faa940c653edee0269e787099936dc98a8b2","family_id":"qf-finite-event-occurrence","seed":20261138,"semantic_template":"qf-finite-event-occurrence/{\"E\":[77,79],\"F\":\"P(S)\",\"S\":[77,78,79],\"x\":77}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={77, 78, 79}, F=P(S), and E={77, 79}. The observed outcome is 77. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"77 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0021","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e924b7fc809a0b5a0c090acb955726802fb6b56502930e47cef745a2b402f01","family_id":"qf-finite-event-occurrence","seed":20261139,"semantic_template":"qf-finite-event-occurrence/{\"E\":[82],\"F\":\"P(S)\",\"S\":[81,82,83],\"x\":81}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={81, 82, 83}, F=P(S), and E={82}. The observed outcome is 81. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"81 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0022","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"810d29e6e919ed876b0df0fc59fb19f4dd03c05cc5a77764a707c3e3c681ad6f","family_id":"qf-finite-event-occurrence","seed":20261140,"semantic_template":"qf-finite-event-occurrence/{\"E\":[85,87],\"F\":\"P(S)\",\"S\":[85,86,87],\"x\":85}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={85, 86, 87}, F=P(S), and E={85, 87}. The observed outcome is 85. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"85 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0023","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5c057bcfcf2f4f47101d423a79858209f587d65a57d1f98b87ea05c0108da22c","family_id":"qf-finite-event-occurrence","seed":20261141,"semantic_template":"qf-finite-event-occurrence/{\"E\":[90],\"F\":\"P(S)\",\"S\":[89,90,91],\"x\":89}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={89, 90, 91}, F=P(S), and E={90}. The observed outcome is 89. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"89 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0024","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7c9275eaf7a638955e44608e87396c331b11ef62dcaf6a139db7ea05663c6fea","family_id":"qf-finite-event-occurrence","seed":20261142,"semantic_template":"qf-finite-event-occurrence/{\"E\":[93,95],\"F\":\"P(S)\",\"S\":[93,94,95],\"x\":93}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={93, 94, 95}, F=P(S), and E={93, 95}. The observed outcome is 93. Does E occur?","answer":{"kind":"choice","value":"Yes","choices":["Yes","No"],"explanation":"93 belongs to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-occurrence-0025","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"1b800562f40f96282bbb70a8310a41cf03d6156b0ac6bf1c398bf2d92f5773ea","family_id":"qf-finite-event-occurrence","seed":20261143,"semantic_template":"qf-finite-event-occurrence/{\"E\":[98],\"F\":\"P(S)\",\"S\":[97,98,99],\"x\":97}"},"fields":{"title":"Occurrence of a Finite Event","stem":"Let S={97, 98, 99}, F=P(S), and E={98}. The observed outcome is 97. Does E occur?","answer":{"kind":"choice","value":"No","choices":["Yes","No"],"explanation":"97 does not belong to E. No probability is assigned in this question."},"skills":["event occurrence"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0001","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"f542aa8495bd3dcb4d3227ca525413c7d7b391dbfab2bb8e3575936166769cf9","family_id":"qf-finite-event-cardinality","seed":20261219,"semantic_template":"qf-finite-event-cardinality/{\"E\":[2],\"F\":\"P(S)\",\"S\":[1,2,3]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={1, 2, 3}, F=P(S), and E={2}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0002","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d17aa62f31110e432774cee9ee5ee7729b4262762c844d69848c6d0a17d2b4d7","family_id":"qf-finite-event-cardinality","seed":20261220,"semantic_template":"qf-finite-event-cardinality/{\"E\":[5,7],\"F\":\"P(S)\",\"S\":[5,6,7]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={5, 6, 7}, F=P(S), and E={5, 7}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0003","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e09bcec3e5fd6f7de4f7336aca6c58486f7614c8978d5be324a0ad0bb075ae9","family_id":"qf-finite-event-cardinality","seed":20261221,"semantic_template":"qf-finite-event-cardinality/{\"E\":[10],\"F\":\"P(S)\",\"S\":[9,10,11]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={9, 10, 11}, F=P(S), and E={10}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0004","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ed5016dc947587039e15c443969955e15a4b49868a75068f765c76fbe7762b5b","family_id":"qf-finite-event-cardinality","seed":20261222,"semantic_template":"qf-finite-event-cardinality/{\"E\":[13,15],\"F\":\"P(S)\",\"S\":[13,14,15]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={13, 14, 15}, F=P(S), and E={13, 15}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0005","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"049bf9c403474e4e2ed7498ffe9d6d26a0481159a40c8b22ffc75bc3d19446c0","family_id":"qf-finite-event-cardinality","seed":20261223,"semantic_template":"qf-finite-event-cardinality/{\"E\":[18],\"F\":\"P(S)\",\"S\":[17,18,19]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={17, 18, 19}, F=P(S), and E={18}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0006","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"23c953826086af73622576dbfde4d95e80de9cad6dd9b83babf126bf01890127","family_id":"qf-finite-event-cardinality","seed":20261224,"semantic_template":"qf-finite-event-cardinality/{\"E\":[21,23],\"F\":\"P(S)\",\"S\":[21,22,23]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={21, 22, 23}, F=P(S), and E={21, 23}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0007","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"6717681ec5607f400a4ec88b44b3ad44446c8139ffaaac78804979c73b2ba929","family_id":"qf-finite-event-cardinality","seed":20261225,"semantic_template":"qf-finite-event-cardinality/{\"E\":[26],\"F\":\"P(S)\",\"S\":[25,26,27]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={25, 26, 27}, F=P(S), and E={26}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0008","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"30c78aa78b5f621994e52cb85a26d4d6ceab4c7dee3dd38e6fafd900c2936878","family_id":"qf-finite-event-cardinality","seed":20261226,"semantic_template":"qf-finite-event-cardinality/{\"E\":[29,31],\"F\":\"P(S)\",\"S\":[29,30,31]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={29, 30, 31}, F=P(S), and E={29, 31}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0009","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e9f1fd6865ea2acf31ad83894968976d9576f60d1a5c53b7d6d086a4865aa8a1","family_id":"qf-finite-event-cardinality","seed":20261227,"semantic_template":"qf-finite-event-cardinality/{\"E\":[34],\"F\":\"P(S)\",\"S\":[33,34,35]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={33, 34, 35}, F=P(S), and E={34}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0010","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"367eb1a8c2560d6ed131fddda27ac3c6cd211e14e1d6ac69bf520debd0722147","family_id":"qf-finite-event-cardinality","seed":20261228,"semantic_template":"qf-finite-event-cardinality/{\"E\":[37,39],\"F\":\"P(S)\",\"S\":[37,38,39]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={37, 38, 39}, F=P(S), and E={37, 39}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0011","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"5d2039dce2a2d8b449bc5cc0c8f6843c906576f9e540e6aed3489a910f6eac72","family_id":"qf-finite-event-cardinality","seed":20261229,"semantic_template":"qf-finite-event-cardinality/{\"E\":[42],\"F\":\"P(S)\",\"S\":[41,42,43]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={41, 42, 43}, F=P(S), and E={42}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0012","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"32b71645bae6d13874ca8c721250bac72c73272da2159436a02db4ad4bdf0be3","family_id":"qf-finite-event-cardinality","seed":20261230,"semantic_template":"qf-finite-event-cardinality/{\"E\":[45,47],\"F\":\"P(S)\",\"S\":[45,46,47]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={45, 46, 47}, F=P(S), and E={45, 47}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0013","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ee4a71b1b0d396d2ba55a80d483e1544be1879b1256dc64b68f7014af9f83fc8","family_id":"qf-finite-event-cardinality","seed":20261231,"semantic_template":"qf-finite-event-cardinality/{\"E\":[50],\"F\":\"P(S)\",\"S\":[49,50,51]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={49, 50, 51}, F=P(S), and E={50}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0014","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d301385967ba06b21c99d70a73e4c15065976f8ee722fba40d9b8c3f50ac3473","family_id":"qf-finite-event-cardinality","seed":20261232,"semantic_template":"qf-finite-event-cardinality/{\"E\":[53,55],\"F\":\"P(S)\",\"S\":[53,54,55]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={53, 54, 55}, F=P(S), and E={53, 55}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0015","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"7126add4a08e68884aa549aca5383ed63b0c120824e2d9e8aedfc1e8bc8f9e9e","family_id":"qf-finite-event-cardinality","seed":20261233,"semantic_template":"qf-finite-event-cardinality/{\"E\":[58],\"F\":\"P(S)\",\"S\":[57,58,59]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={57, 58, 59}, F=P(S), and E={58}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0016","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a44efd73d63526f4e73cf115d474a8e68806241902e360544c4b4c01af6407a6","family_id":"qf-finite-event-cardinality","seed":20261234,"semantic_template":"qf-finite-event-cardinality/{\"E\":[61,63],\"F\":\"P(S)\",\"S\":[61,62,63]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={61, 62, 63}, F=P(S), and E={61, 63}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0017","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"8e5d3e61cf3640beea12bbbe75c482f0b7a419a54862693b6a1c2e51181ae8d3","family_id":"qf-finite-event-cardinality","seed":20261235,"semantic_template":"qf-finite-event-cardinality/{\"E\":[66],\"F\":\"P(S)\",\"S\":[65,66,67]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={65, 66, 67}, F=P(S), and E={66}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0018","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ca9fdb9c8c18242ddd25095e210e5efc50ae78f80c6d79305e7af9e56df41b3d","family_id":"qf-finite-event-cardinality","seed":20261236,"semantic_template":"qf-finite-event-cardinality/{\"E\":[69,71],\"F\":\"P(S)\",\"S\":[69,70,71]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={69, 70, 71}, F=P(S), and E={69, 71}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0019","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"0ef222057ed31fd7144b3dc42f6c76ec37a94bacaf755f3b9f70614de320b733","family_id":"qf-finite-event-cardinality","seed":20261237,"semantic_template":"qf-finite-event-cardinality/{\"E\":[74],\"F\":\"P(S)\",\"S\":[73,74,75]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={73, 74, 75}, F=P(S), and E={74}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0020","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"ba01d871a1def377bbcb3d925093e9f9f65bf058dc519d4a6772716c079a9fdf","family_id":"qf-finite-event-cardinality","seed":20261238,"semantic_template":"qf-finite-event-cardinality/{\"E\":[77,79],\"F\":\"P(S)\",\"S\":[77,78,79]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={77, 78, 79}, F=P(S), and E={77, 79}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0021","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"e22e0839ccbbecd9c97cc0929d8c15c3fadb6929f42f62a08d302c290fb05a27","family_id":"qf-finite-event-cardinality","seed":20261239,"semantic_template":"qf-finite-event-cardinality/{\"E\":[82],\"F\":\"P(S)\",\"S\":[81,82,83]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={81, 82, 83}, F=P(S), and E={82}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0022","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"d7530c6b7b55e7bb678a2537cd5fbf72d38857c22ce98743325a89426570b51e","family_id":"qf-finite-event-cardinality","seed":20261240,"semantic_template":"qf-finite-event-cardinality/{\"E\":[85,87],\"F\":\"P(S)\",\"S\":[85,86,87]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={85, 86, 87}, F=P(S), and E={85, 87}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0023","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"a93337586e2dce404cf8bbb454170a31f46edeb9634fcfce159d12fb6b2ad3a0","family_id":"qf-finite-event-cardinality","seed":20261241,"semantic_template":"qf-finite-event-cardinality/{\"E\":[90],\"F\":\"P(S)\",\"S\":[89,90,91]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={89, 90, 91}, F=P(S), and E={90}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0024","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"35efabf3696ba26e5ac9f4543eb14d823bb975034165925ef808bbec54455ae5","family_id":"qf-finite-event-cardinality","seed":20261242,"semantic_template":"qf-finite-event-cardinality/{\"E\":[93,95],\"F\":\"P(S)\",\"S\":[93,94,95]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={93, 94, 95}, F=P(S), and E={93, 95}. What is the cardinality of E?","answer":{"kind":"numeric","value":2,"explanation":"E contains 2 distinct outcomes. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}
{"schema_version":"ocme-question-localization-v0.1","question_id":"q-20260918-finite-event-cardinality-0025","batch_id":"batch-20260918-finite-events","locale":"en","translation_state":"ai_candidate","source":{"question_sha256":"cec267b81e96915976eefefc54fe7afc8180569362441b0312fe898dbe2212d2","family_id":"qf-finite-event-cardinality","seed":20261243,"semantic_template":"qf-finite-event-cardinality/{\"E\":[98],\"F\":\"P(S)\",\"S\":[97,98,99]}"},"fields":{"title":"Cardinality of a Finite Event","stem":"Let S={97, 98, 99}, F=P(S), and E={98}. What is the cardinality of E?","answer":{"kind":"numeric","value":1,"explanation":"E contains 1 distinct outcome. This is a cardinality, not a probability."},"skills":["event cardinality"],"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."}}