*3. You face a decision problem involving three states of nature with prior probabilities Pr(a1) = .15, Pr(a2) = .30, and Pr(a3) = .55. To gain further information, you consult an expert who gives you a forecast (z) with conditional probabilities: Pr(z|a1) = 0.30; Pr(z|a2) = 0.50; Pr(z|a3) = 0.10. If you are a Bayesian learner, what probabilities do you want to use in your decision