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Let A1, ... ,20 be independent events each with probability 1/2. Let X be the number...

Let A1, ... ,20 be independent events each with probability 1/2. Let X be the number of events among the first 10 which occur and let Y be the number of events among the last 10 which occur. Find the conditional probability that X = 5, given that X + Y = 12.

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