ODDLY LIKELY
ODDLY LIKELY
How many people do you need in a room before two of them probably share a birthday? Move the slider.
Better than a coin flip — with just 23 people.
Chance that at least two people share a birthday, by group size. Hover to read any point.
Most people answer around 183, which is half of 365. That would be the right answer to a different question: how many people you need before someone shares your birthday.
The real question doesn't single anyone out. Any two people in the room can match, so what matters is the number of pairs, not the number of people. Ten people make 45 pairs. Twenty-three people make 253 pairs — and 253 chances for a match is plenty.
It's easier to work out the chance that nobody matches, then subtract from 1. The second person must avoid 1 birthday, the third must avoid 2, and so on:
With n = 23 that gives 49.3% for no match, so the chance of at least one shared birthday is 50.7%.
| People | Chance two share a birthday |
|---|---|
| 10 | 11.7% |
| 23 | 50.7% |
| 30 | 70.6% |
| 50 | 97.0% |
| 57 | 99.0% |
| 70 | 99.9% |
Assumes 365 equally likely birthdays and ignores 29 February. Real birthdays cluster slightly by season, which makes matches marginally more likely.