5. (12 points) (a) A gambler has in his pocket a fair coin and a two-headed coin (i.e, both sides of the coin are heads). He selects one of the coins at random, and when he flips it, it shows heads. What is the probability that it is the fair coin? (b) Suppose that he flips the same coin a second time and again it shows heads. Now what is the probability that it is the fair coin? (Note: For a fair coin, each coin flip results in heads or tails with equal probability irrespective of the outcomes of past flips.) (c) Suppose that he flips the same coin a third time and it shows tails. Now what is the probability that it is the fair coin