The Birthday Paradox

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.

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, Concepts and Questions to Start Background Research

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?