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In probability theory, the birthday problem or birthday paradox concerns the probability that, in a set of
n
{\displaystyle n}
randomly chosen people, some pair of them will have the same birthday. By the pigeonhole principle, the probability reaches 100% when the number of people reaches 366 (since there are only 365 possible birthdays, excluding February 29). However, 99.9% probability is reached with just 70 people, and 50% probability with 23 people. These conclusions are based on the assumption that each day of the year (except February 29) is equally...