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.
Compute P(A1 B).
Compute P(A2 B).
Compute P(B).
Apply Bayes' theorem to compute P(A1 | B) (to 4 decimals).
Also apply Bayes' theorem to compute P(A2 | B) (to 4 decimals).