Which formula represents Bayes' theorem for P(A|B) in terms of P(B|A), P(A), and P(B)?

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Multiple Choice

Which formula represents Bayes' theorem for P(A|B) in terms of P(B|A), P(A), and P(B)?

Explanation:
Bayes' theorem lets you update the probability of A after seeing B. It follows from the definition of conditional probability: P(A|B) = P(A ∩ B)/P(B). The joint probability P(A ∩ B) can be written as P(B|A) P(A). Plugging in gives P(A|B) = [P(B|A) P(A)] / P(B). This is the form for expressing P(A|B) in terms of P(B|A), P(A), and P(B). The other expressions mix up the terms or introduce circulars, so they don’t represent the correct relationship.

Bayes' theorem lets you update the probability of A after seeing B. It follows from the definition of conditional probability: P(A|B) = P(A ∩ B)/P(B). The joint probability P(A ∩ B) can be written as P(B|A) P(A). Plugging in gives P(A|B) = [P(B|A) P(A)] / P(B). This is the form for expressing P(A|B) in terms of P(B|A), P(A), and P(B). The other expressions mix up the terms or introduce circulars, so they don’t represent the correct relationship.

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