Five persons are in a room. What is the probability that at least 2 of them were born in the same birth month?

To keep things simple let's assume that each person has a 1/12 probability of being born in each month. The probability that all five people are born in different months is (11/12)*(10/12)*(9/12)*(8/12) = 0.381944. So the probability of a common month is 1 - 0.381944 = 0.618056.