In probability theory, the birthday problem or

**birthday paradox**concerns the probability that, in a set of

**randomly chosen people, some pair of them will have the same birthday. By the**

*n**pigeonhole principle*, the probability reaches 100% when the number of people reaches 367 (since there are only 366 possible birthdays, including 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 probable for a birthday.

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