The prior probabilities for events a1, a2, and a3 are p(a1) = 0.20, p(a2) = 0.30, and p(a3) = 0.50. the conditional probabilities of event b given a1, a2, and a3 are p(b | a1) = 0.20, p(b | a2) = 0.40, and p(b | a3) = 0.30. (assume that a1, a2, and a3 are mutually exclusive events whose union is the entire sample space.) a. compute p(b