Minetoo

How many people do you need at a party to have a 50/50 chance that two of them share a birthday?

Most people would say "lots". At first sight, it seems like there's little chance of finding two people in a small group sharing the same birthday. After all, if you meet a random stranger on the street, there's just a 1 in 365 chance that they'll share your birthday.

The answer is that you only need 23 people.

The fact that the number is so low is known as the Birthday Paradox, as it seems somehow paradoxical that there's actually such a high chance of something apparently so unlikely.

As it turns out, the reason it catches so many people out is that you're not actually asking the question you think you're asking. You're not asking how many people share your birthday, you're asking if anyone shares anyone else's birthday.

Let's consider each person at the party in turn. Each of them is asking 22 other people if they share their birthday. So in total, that's 253 pairs of people who potentially share their birthday. How did we get that number? Multiply 23 by 22, then divide by two because there's only one question asked per pair. That's over half of 365, so there's a reasonable chance that at least one pair will have the same birthday.

We've simplified the maths a bit, and ignored the fact that birthdays are not evenly distributed over the year. If you're interested in finding out more, searching on Google for "Birthday Paradox" will give you a more technical perspective on the problem.

Minetoo can go a few steps further than the Birthday Paradox. Minetoo's "MEB" function matches you on your exact birthdate, including your year of birth, with all the members of Minetoo's rapidly growing MEB community.