Question

What is the probability that in a group of n people, n > 12, at least two will have the same birth month?

Answer 1

The probability that at least 2 will have the same birth month = 1 - Probability that none of the n people will have same birth month.

Now, if n > 12, the probability that none of the n people will have same birth month is = 0, as, if n = 13 say, then even if 12 people have different birth months, the 13th people will share his/her birth month with any one of the other 12 people. It is true for any n > 12.

Hence, the probability that at least 2 will have same birth month = 1 - 0 = 1. (Ans).