Answer
$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$.
Explanation
By law of total probability, the denominator can be expressed as $P(B) = P(B|A)P(A) + P(B|A^c)P(A^c)$.
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In probability theory, what is Bayes' Theorem for finding the posterior probability $P(A|B)$?
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