a. A gambler has a fair coin and a two-headed coin in his pocket. He selects one

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a. A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random; 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?

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?

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