What is the chance that two people have the same birthday?

Suppose you have 367 people together in a room, at a party, or a conference. Since there are only 366 possible birthdays, you can be absolutely sure that at least one pair of people has the same birthday.

But what about smaller groups of people. How many people does it take in the same room for there to be a 50% chance that two have the same birthday?

We are going to assume that all birthdays are equally likely, and we are going to ignore, for the moment, 29th February.

Let p(n) be the probability of at least two people in the same room having the same birthday. The probability that no-one has the same birthday is easier to calculate, and is 1-p(n)

Imagine people coming into the room one at a time. It doesn't matter who comes in first - if there is only one person then the probability that no pair of people have the same birthday is 1.

The second person can have any birthday except the birthday of the first person, 364 possibilities. So -mathformula not MarkupType-
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