In a room of 23 people, what is the chance that two people share the same birthday?

Why is this called a paradox?

What does the number 253 refer to?

Discussion Questions: Do you know any other interesting paradoxes? If you do, share one. If you don’t, look some up and share one with a friend.

show Answershide Answers

The Birthday Paradox
In a classroom of 23 people, there is a 50-50 chance that two of them have the same birthday. This is called the Birthday Paradox (also known as The Birthday Problem). While it may seem senseless that two people out of 23 share a birthday, it is actually quite probable. The reason it seems unlikely is because of how you think of it. You think that it’s unlikely that you have the same birthday as someone else. You don’t think about the chances of the other 22 people in the room. If you think of it that way, you can see how the probability greatly increases. The first person has 22 chances to find a match on the attendance list. The second person only has 21 chances. When you get to the end of the list, you can add up all of the chances. Eventually, you find that there are 253 chances of finding matching birthdays in a random class of 23 people. Next time you’re in a group of 20-30 people, test out this probability theory.

In a room of 23 people, there is a 50-50 chance that two people share the same birthday.

This is called a paradox because it seems senseless, but it’s true.

The number 253 refers to the number of chances of finding matching birthdays in a group of 23 people.