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Probability
The birthday paradox
Usually credited to Richard von Mises in 1939; a standard exercise in Feller's 1950 textbook.
Put 23 people in a room, chosen with no regard to when they were born. Assume every one of the 365 days of the year is equally likely as a birthday and ignore 29 February. You are not asking whether anyone shares your birthday. You are asking whether any two people in the room, any pair at all, share one.
How likely is it that at least two of the 23 share a birthday?