Birth Month Puzzle

We can solve this by finding the probability that they each have different birth months:

First person: There’s a 100% chance that they are born in one of the 12 months.
Second person: Must be born in a different month than the first person. The probability of this is 11/12.
Third person: Must be born in a different month than the first two people. The probability of this is 10/12.
Fourth person: Must be born in a different month than the first three people. The probability of this is 9/12.

The probability of them all having different birth months
= 1 x 11/12 x 10/12 x 9/12
= 990/1728
= 55/96

There’s a 55/96 chance they all have different birth months.

To find the probability that they don't all have different birth months (in other words, that at least two of them have the same birth month), we subtract this from 1.

1 - 55/96
= 41/96

There is a 41/96, or about 43%, chance that two or more of the people share a birth month.

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