The shared birthday question...

Category: Statistics

Published: 01/13/2009 06:39 a.m.

*This was showcased to me by listening to Shirky on Coase. Interesting stuff.

Imagine a normal classroom with 30 students in it. Someone in the class asks you to bet $100 that two people in the room share a birthday. Most people would (mistakenly) take that bet in a heartbeat. Here is the wrong logic they use.

There are 30 people in the class. There are 365 possible birthdays. So, there is about a 1-10 chance that two people share a birthday. So someone would for sure bet that no two people have a shared birthday. WRONG.

This kind of thinking answers a different question. It is the logic if someone bet you what the odds are that someone in the class shares a birthday with you. This is different.

The correct way addresses the network. For every person (or every birthday), there are 29 other possible connections. The real math is the summation of 1 to 29. So the total number of possible matches is 435. This is greater than 365. So in the odds game, chances are very likely that one of those is a match. It is tricky, but that is the way it works. You are looking at the comparisons, and there are much more of those than people.

This used to be a real mystery to me. In both my home in Cincinnati and in Katy, there was someone across the street that shared my birthday. I always thought this was far more unique than it really is. It is odd that it is my birthday at both locations, but to have two people in a cul-de-sac share a birthday is not really that strange at all.

I love tricky math questions like this, and I have a couple more in draft-mode that will hopefully be done soon such as a bad bet question, the "Let's make a deal" question from the movie 21, and a bit on my experience with roulette, and why is it such a money-maker for casinos.