Same Birthday |
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For a group size of n, the probability that all people have a different Birthday = $\frac{364}{365}\times\frac{363}{365}\times\frac{362}{365}...\frac{366-n}{365}$ = p
The probability that at least one pair share a birthday = 1 - p
Number of People | Chance of no pairs | Chance of at least one pair |
1 | 1 | 0 |
2 | 0.997 | 0.003 |
3 | 0.992 | 0.008 |
4 | 0.984 | 0.016 |
. | ... | ... |
22 | 0.524 | 0.476 |
23 | 0.493 | 0.507 |
If there are 23 or more (randomly chosen) people in a group then there is a more than even chance that two will share a birthday.