Compute the probability that at least two people in a group share a birthday.
The birthday problem asks: in a group of n people, what is the probability that at least two share the same birthday? The result is surprisingly high — with just 23 people, the probability exceeds 50%. This counterintuitive result arises because we check all possible pairs, not just one pair.
P(match) = 1 − (365/365 × 364/365 × ... × (365−n+1)/365)
Because the result is counterintuitive: most people guess you'd need far more than 23 people for a 50% chance of a shared birthday. It's surprising because we're checking all pairs, and 23 people form 253 pairs.
About 57 people are needed for a 99% probability of at least one shared birthday.