40. (a) A gambler has in his pocket a fair coin and a two-headed coin. He selects...
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40.
(a) A gambler has in his pocket a fair coin and a two-headed coin. 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?
(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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