birthday problem

In a room of n people, the probability of at least two sharing a birthday is surprisingly high. With just 23 people, it's over 50%.

P(match) = 1 − 365!/(365ⁿ · (365−n)!)

This counterintuitive result illustrates the birthday paradox — the number of possible pairs grows as n(n−1)/2, much faster than n itself.

references

DasGupta. "The matching, birthday and strong birthday problem: a contemporary review." Journal of Statistical Planning and Inference, 2005.

Wendl. "Collision probability between sets of random variables." Statistics & Probability Letters, 2003.