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The prior probabilities for events A1, A2, and A3 are P(A1) = 0.20, P(A2) = 0.50, and P(A3) = 0.30. The conditional probabilities of event B given A1, A2, and A3 are P(B | A1) = 0.50, P(B | A2) = 0.40, and P(B | A3) = 0.30.
a. Compute P(B ( A1), P(B (A2), and P(B ( A3).
b. Apply Bayes’ theorem, equation (2.16), 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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