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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 = EQN:\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 |

| 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.