# Same Birthday

What is the smallest group size that would give a better that even chance of two people sharing the same birthday?

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.