Question: The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The conditional probabilities of event

The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The conditional probabilities of event B given A1, A2, and A3 are P(B | A1) 5 .50, P(B | A2) = .40, and P(B | A3) = .30.

a. Compute P(B ( A1), P(B ( A2), and P(B ( A3).

b. Apply Bayes’ theorem, equation (4.19), to compute the posterior probability P(A2| B).

c. Use the tabular approach to applying Bayes’ theorem to compute P(A1| B), P(A2| B), and P(A3| B).

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