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

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33.

(a) A gambler has in his pocket a fair coin and a two-headed coin. 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. What is now the probability that it is the fair coin?

(c) Suppose that he flips the same coin a third time and it shows tails. What is now the probability that it is the fair coin?

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