Suppose that there are two people in a room. The probability that they share the same birthday (date, not necessarily year) is 1/365, and the probability that they have different birthdays is 364/365. To illustrate, suppose that you’re in a room with one other person and that your birthday is July 1. The probability that the other person does not have the same birthday is 364/365 because there are 364 days in the year that are not July 1. If a third person now enters the room, the probability that he or she has a different birthday from the first two people in the room is 363/365. Thus, the probability that three people in a room having different birthdays is (364/365) (363/365). You can continue this process for any number of people.
Find the number of people in a room so that there is about a 50% probability that at least two have the same birthday.’