# The Birthday Problem: A short lesson in probability.

*Last revised 8/24/05*

## Introduction with simulation

**Happy Birthday!** There's a birthday in your class today! Or
will there be two? How likely is it that two people in your class
have the same birthday? Say your class has 28 students.

There are a number of ways to approach this problem. The most
common is to take a survey and see if it happens that two birthdays
fall on the same day. But if it happens in the surveyed class, will
it occur in another class with different students? The question of
how likely it is for any given class is still unanswered.

Another way, is to survey more and more classes to get an idea of
how often the match would occur. This can be time consuming and may
require a lot of work. But a computer can help out. Below is a
simulation of the birthday problem. It takes a little while (about 25
seconds) to respond, but it will generate a random list of birthdays
time after time.

Choose a number for your class size and do
10 trials with that size.

Applet Source, Written by Nicholas Exner, modified by Michael McKelvey.

Now what do you think the probability of a match is?

* For more information on the mathematics of this problem, see

Mosteller, F. (1965). __Fifty challenging problems in probability with solutions__. New York, NY: Dover Publications, Inc., pp. 46-49.