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Answers for “为什么交换 A 和 B 通常会改变答案?”

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Swapping the events changes both the numerator and the denominator in the conditional probability formula. P(A∣B)P(A\mid B) uses P(A∩B)P(A \cap B) as the numerator and P(B)P(B) as the denominator, whereas P(B∣A)P(B\mid A) uses P(A∩B)P(A \cap B) as the numerator but P(A)P(A) as the denominator.

Conditions: Events A and B have different marginal probabilities (P(A)≠P(B)P(A) \neq P(B)).; Both events have positive probability.