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In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of $n$ randomly chosen people, some pair of them will have the same birthday.

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The events "$k$ people have a birthday on Jan 1" and "$k$ people have a birthday on Jan 2" are not mutually exclusive, and so the probability that either of them occurs is not equal to the sum of thei …
answered Mar 22 '12 by Martin O'Leary