FRIDAY'S KILLER QUESTION: You are in a room full of people and you ask them all when their birthday is...

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We'll add the correct answer to the bottom of this article on Monday afternoon.

You are in a room full of people, and you ask them all when their birthday is. How many people must there be for there to be a greater than 50% chance that at least two will share the same birthday?

ANSWER:

It is easier to ask what the chances of two people not having the same birthday are. So suppose that there are just the two people in the room, what are the chances of them not having the same birthday? There are 364 days out of 365 days that the second person could have, so the probability is 364/365. If there are three people in the room the second must have a birthday on one of 364 out of 365, and the third must have one of the remaining 363 out of 365. So the probability is then

And so on. If there are n people in the room the probability of no two sharing a birthday is

So the question becomes, what is the smallest n for which this is less than one half? And the answer is 23.