Bill is a student at Cornell. In any given course he gets an A with probability 1/2

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Bill is a student at Cornell. In any given course he gets an A with probability 1/2 and a B with probability 1/2. Suppose the outcomes of his courses are independent. In his 4 years at Cornell he will take 33 courses. If he can get 22 A’s and only 11 B’s he can graduate with a 3.666 average. What is the probability that he will do this?

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