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Combinatorics 4.0/10

Birthday Paradox

Assuming birthdays are uniformly distributed across 365 days and ignoring leap years, what is the minimum number of people needed in a room such that the probability of at least two sharing a birthday exceeds 50%?

Related problems & prerequisites

Worth solving first

Source: Classic result popularised by Richard von Mises (1939); standard in probability texts. Statement written for AxiomIQ.