Jack has three coins C1, C2, and C; with p1, p2, and p3 as their corresponding probabilities of landing heads. Jack flips coin C1 twice and then decides, based on the outcome, whether to flip coin C2 or C3 next. In particular, if the two C1 flips come out the same, Jack flips coin C2 three times next. However, if the C1 flips come out different, he flips coin C3 three times next. Given the outcome of Jack's last three flips, we want to know whether his first two flips came out the same. Describe a Bayesian network and a corresponding query that solves this problem. What is the solution to this problem assuming that p1 =.4, p2= .6, and p3= .1 and the last three flips came out as follows:
(a) tails, heads, tails.
(b) tails, tails, tails