The Birthday Paradox
With only 23 people in a room there is a 50.7% probability that at least two of them share a birthday. With 70 people it exceeds 99.9%. The exact probability for n people is:
P(n) = 1 − (365/365) × (364/365) × … × ((365−n+1)/365)
This feels counterintuitive because we compare every pair, not just one person — so with 23 people there are already C(23,2) = 253 pairs to compare.
With only 23 people in a room there is a 50.7% probability that at least two of them share a birthday. With 70 people it exceeds 99.9%. The exact probability for n people is:
P(n) = 1 − (365/365) × (364/365) × … × ((365−n+1)/365)
This feels counterintuitive because we compare every pair, not just one person — so with 23 people there are already C(23,2) = 253 pairs to compare.