Home Project Ideas Project Guide Ask An Expert Blog Careers Teachers Parents Students

The Birthday Paradox

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

Abstract

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.

Objective

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.

Share your story with Science Buddies!

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


Last edit date: 2013-01-10

Introduction

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

Bibliography

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

http://en.wikipedia.org/wiki/Birthday_paradox

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.

Ask an Expert

The Ask an Expert Forum is intended to be a place where students can go to find answers to science questions that they have been unable to find using other resources. If you have specific questions about your science fair project or science fair, our team of volunteer scientists can help. Our Experts won't do the work for you, but they will make suggestions, offer guidance, and help you troubleshoot.

Ask an Expert

Related Links

If you like this project, you might enjoy exploring these related careers:

person graphing data on computer screen

Statistician

Statisticians use the power of math and probability theory to answer questions that affect the lives of millions of people. They tell educators which teaching method works best, tell policy-makers what levels of pesticides are acceptable in fresh fruit, tell doctors which treatment works best, and tell builders which type of paint is the most durable. They are employed in virtually every type of industry imaginable, from engineering, manufacturing, and medicine to animal science, food production, transportation, and education. Everybody needs a statistician! Read more
Mathematician at work

Mathematician

Mathematicians are part of an ancient tradition of searching for patterns, conjecturing, and figuring out truths based on rigorous deduction. Some mathematicians focus on purely theoretical problems, with no obvious or immediate applications, except to advance our understanding of mathematics, while others focus on applied mathematics, where they try to solve problems in economics, business, science, physics, or engineering. Read more
female actuary making calculations

Actuary

Life is full of risks to both people and property. Actuaries predict the chances that future negative events will occur in a person's life, and then think of ways to reduce those chances, or reduce the impact of those negative events. Actuaries help bring peace of mind to both families and to businesses. Read more
math teacher helping student at blackboard

Math Teacher

Math teachers love mathematics and understand it well, but much more than that, they enjoy sharing their enthusiasm for the language of numbers with students. They use a variety of tools and techniques to help students grasp abstract concepts and show them that math describes the world around them. By helping students conquer fears and anxieties about math, teachers can open up many science and technology career possibilities for students. Teachers make a difference that lasts a lifetime! Read more