(Solution) - The prior probabilities for events A1 and A2 are P A1 -(2025 Original AI-Free Solution)

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The prior probabilities for events A1 and A2 are P(A1) = .40 and P(A2) = .60. It is also known that P(A1 ( A2) = 0. Suppose P(B | A1) = .20 and P(B | A2) = .05.
a. Are A1 and A2 mutually exclusive? Explain.
b. Compute P(A1 ( B) and P(A2 ( B).
c. Compute P(B).
d. Apply Bayes' theorem to compute P(A1 | B) and P(A2 | B).