Carnegie Mellon University 10 601 Problem 1: More Probability Review (a) [4 Points] For events A and B, prove P(AjB) = P(BjA)P(A) P(B) : Solution: This is Bayes theorem. From the chain rule, we have that P(A; B) = P(AjB)P(B) and P(A; B) = P(BjA)P(A). Therefore, P(AjB)P(B) = P(BjA)P(A). Rearranging gives the desired equality. (b) [4 ...[Show More]

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