The Birthday Paradox

Q: What is the minimum number of people required in group to have a better than 50% chance that two will share a birthday?

A: Just 23

How Many People Need to Be in a Group Before Two Share a Birthday?

At first glance, it seems like you'd need a fairly large group to find two people with the same birthday. After all, there are 365 days in a year (ignoring leap years), so how likely could a match really be?

Surprisingly, the answer is just 23 people.

This is known as the Birthday Paradox—a counterintuitive probability puzzle that shows how human intuition often clashes with mathematics. In a group of 23 randomly selected individuals, there's a greater than 50% chance that at least two people share a birthday. The reason for this isn't about comparing everyone to your own birthday—it's about comparing everyone to everyone else. In a group of 23, there are 253 possible pairs of people, and each pair is a new chance for a shared birthday.

As the group gets larger, the probability rises quickly. With 30 people, the chance of a shared birthday jumps to about 70%. At 57 people, it's over 99%.

So the next time you're at a party or in a classroom with 23 or more people, don’t be surprised if two of them blow out candles on the same day each year.