{"schema_version":"ocme-site-results-v1","locale":"en","page_type":"derivations","facts":{"questions":36000,"reviewed":36000,"display_candidates":0,"knowledge":302,"guides":299,"paths":59,"batches":360,"families":1441,"atlas":302,"core":80,"evidence":9,"formal_evidence":5,"formal_subjects":4,"lean_files":6,"lean_toolchain":"leanprover/lean4:v4.30.0","question_state":"candidate","english_state":"ai_candidate","question_Lean":"NOT_RUN","canonical_truth_promotion":false},"filters":{"q":"mko-conditional-probability"},"kind":"guides","total":1,"pages":1,"page":1,"entries":[{"id":"derivation-mko-conditional-probability-01","title":{"zh-Hant":"有限模型的條件機率：正分母、兩個方向與零機率條件","en":"Conditional probability in finite models: positive denominators, the two directions and null conditioning events"},"summary":{"zh-Hant":"在 S={1,2,3,4,5,6}、權重 w=(1,2,3,2,4,0)/12 的有限模型中，設 A={2,3}、B={3,4,5,6}、Z={6}。驗證模型合法，計算 P(A|B) 與 P(B|A)，與等可能計數比 |A∩B|/|B| 及乘積 P(A)P(B) 比較，並判定 P(A|Z) 是否有定義。","en":"In the finite model on S={1,2,3,4,5,6} with weights w=(1,2,3,2,4,0)/12, let A={2,3}, B={3,4,5,6} and Z={6}. Validate the model, compute P(A|B) and P(B|A), compare them with the equiprobable count ratio |A∩B|/|B| and with the product P(A)P(B), and decide whether P(A|Z) is defined."},"mko_ids":["mko-conditional-probability"]}],"title":"Concept derivation guides"}