# The Birthday Problem

It’s been a couple of weeks since I last posted.  Things have been BUSY!!  I have been Desmos-ing quite a bit, just haven’t had a chance to write about it.  Here’s a little post about one illustration I enjoyed creating on Desmos lately.

In Pre-Calculus, the students at our school are just beginning to learn various counting principles and ways to calculate probabilities.

One of my favorite probability questions is “The Birthday Problem.”  If you’re not familiar with it, here it is:

What is the probability that at least two people in a room with n people in it share the same birthday (not counting year)?

The answer is a bit counter-intuitive (as are many questions in probability).  In fact, in a room with just 23 people in it, the probability of two people having the same birthday is already better than 50%.

Here’s a fun little Desmos graph to illustrate the probability for different values of n (based on a 365 day year).  The black points represent the falling probability that each person in the room has a unique birthday.  The chances that at least two people share a birthday is shown by the green points.

If you’ve never explored this problem before, despite its surprising result, it isn’t terribly challenging to do the calculations.

Wikipedia does a decent job of explaining the problem in more detail,  or you can also go to Wolfram Mathworld for a bit more of a math-intense explanation.  🙂  Loving Desmos!