Suppose that a box contains five coins, and that for each coin there is a different probability that a head will be obtained when the coin is tossed. Let pi denote the probability of a head when the ith coin is tossed (i = 1, 2, 3, 4, 5), and suppose that p1 = 0, p2 = 1/4, p3 = 1/2, p4 = 3/4 and p5 = 1. (a) Suppose that one coin is selected at random from the box and when it is tossed once, a head is obtained. What is the posterior probability that the ith coin was selected (i = 1, 2, 3, 4, 5)? (b) If the same coin were tossed again, what would be the probability of obtaining another head?