answer with explanation

Suppose you own a trucking company with a large eet of trucks. Breakdowns occur randomly in time and the number of breakdowns during an interval of t days is assumed to be Poisson distributed with mean 15A. The parameter A is the daily breakdown rate. The possible values for A are .5, 1, 1.5, 2, 2.5, and 3 with respective probabilities .1, .2, .3, .2, .15, and .05. If one observes y breakdowns, then the posterior probability of A is proportional to g(/\\)e('m (tA)y, where g is the prior probability. 1. If 12 trucks break down in a six-day period, nd the posterior probabilities for the different rate values. 2. Find the probability that there are no breakdowns during the next week