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Answers for “如何将数字代入视频末尾显示的重排贝叶斯公式?”

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Substitute the given numerical values into the rearranged formula P(B|A) = P(B)PP(B)P(A|B)/P(A). For example, if P(B)=1/21P(B) = 1/21, P(A|B) = 4/104/10, and P(A)=24/210P(A) = 24/210, the calculation is (1/21∗4/101/21 * 4/10) / (24/21024/210).

Conditions: The formula used is the rearranged Bayes identity for P(B|A).; The given probabilities must be consistent with the formula's assumptions (e.g., P(A)>0P(A) > 0).

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Starting from the equality P(A)PP(A)P(B|A) = P(B)PP(B)P(A|B), you can solve for either conditional probability by dividing by the corresponding marginal probability. Dividing both sides by P(B)P(B) isolates P(A|B), giving P(A|B) = P(A)PP(A)P(B|A)/P(B).

Conditions: Both A and B have positive probability for the ordinary conditionals used here.; The algebraic rearrangement requires the denominators P(B)P(B) and P(A)P(A) to be nonzero.