Test It in Your Group

Next time you are in a group of 23 or more people, count heads. In any such room, there is a 50% chance that at least two share a birthday. Ask around — you will confirm the paradox roughly half the time.

The math is countable. With n people, the probability of no shared birthday is (365/365) × (364/365) × … × ((365 − n + 1)/365). For n = 23, this product is 0.493, so the chance of a match is 1 − 0.493 = 0.507, just over 50%. Scale up and it climbs fast: 50 people reach 97%, and 70 people reach 99.9%. The reason is the pair count — 70 people form 2,415 distinct pairs, and with that many chances at 1 in 365, a match is nearly inevitable.