Two related experiments are performed. The first has three possible mutually exclusive outcomes: A,B, and C. The second has two possible, mutually exclusive outcomes: X We know P(A) = 0.2 and P(B) = 0.65. We also know the following conditional probabilities if the result of the second experiment is X: P(X|A) = 0.75, P(X|B) = 0.60, and P(X|C) = 0.40. Find P(A|X), P(B|X), and P(C|X). What is the probability that the result of the second experiment is Y?
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