Birthdays

The way to find the probability of at least two birthdays being the same is to calculate the probability that it does not happen - zero people share the same birthday - and then subtract that from 1.

With 365 days/year (ignore leap year) the probability that the first person added to the group does not have the same birthday as someone else already in the group is 365/365 since there is no one else in the group.

For the next person it is 364/365 and for the last person it is 341/365. To find the probability that no two people have the same birthday multiply these probabilities to get 365! /( 340! * 365^25) = 0.4313. ( ! means factorial.)

Subtract that from 1 to get 1-0.4313 = 56.87% which is the probability that at least two members of the group have the same birthday.

Since 365 factorial is an extremely large number it is computationally easier to just evaluate each term. Probability of at least two birthdays = 1 - ((365/365)*(364/365) ... *(341/365))

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Copyright 2002, Larry C. Sanders

Last update 2002.04.12