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The Birthday Paradox

Time Required Very Short (≤ 1 day)
Prerequisites None
Material Availability Readily Available
Cost Very Low (under $20)


This project shows how mathematical probability sometimes contradicts our intuition. Despite the fact that there are 365 days in a year, if you survey a random group of just 23 people there is a 50:50 chance that two of them will have the same birthday. Don't believe it? Try this project and see for yourself.


The objective of this project is to prove whether or not the birthday paradox holds true by looking at random groups of 23 or more people.

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Last edit date: 2013-01-10


The Birthday Paradox states that in a random gathering of 23 people, there is a 50% chance that two people will have the same birthday. Is this really true?

Terms and Concepts

Birthday Paradox, probability theory, converse probability


There are a number of different sites that explain the Birthday Paradox and explain the statistics. Here is one to get you started:


Experimental Procedure

1) First you will need to collect birth dates for random groups of 23 or more people. Ideally you would like to get 10-12 groups of 23 or more people so you have enough different groups to compare. Here are a couple of ways that you can find a number of randomly grouped people.

  • Most schools have around 25 students in a class, so ask a teacher from each grade at your school to pass a list around each of his/her classes to collect the birth dates for students in each of his/her classes.
  • Use the birth dates of players on major league baseball teams. (Note: this information can easily be found on the internet).

2) Next you will need to sort through all the birth dates you have collected and see if the Birthday Paradox holds true for the random groups of people you collected. How many of your groups have two or more people with the same birthday? Based on the birthday paradox, how many groups would you expect to find that have two people with the same birthday?

Share your story with Science Buddies!

I did this project I Did This Project! Please log in and let us know how things went.

Share your story with Science Buddies!

I did this project I Did This Project! Please log in and let us know how things went.

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