(Answered) Question a hat contains 100 coins where at least 99 are

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Question: A hat contains 100 coins, where at least 99 are fair, but there may be one that is doubleheaded (always landing Heads); if there is no such coin, then all 100 are fair. Let D be the event that there is such a coin, and suppose that P(D) = ½. A coin is chosen uniformly at random. The chosen coin is flipped 7 times, and it lands Heads all 7 times.

(a) Given this information, what is the probability that one of the coins is double headed?

(b) Given this information, what is the probability that the chosen coin is double headed?

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