Posts Tagged ‘birthday’

The Chances of Sharing a Birthday

Tuesday, May 27th, 2008

In any given group of people, how many people do you think there need to be in order for there to be a 50% chance of at least two people sharing the same birthday?

365 / 2 = ~183 people?

Nope. Think again. This is not a trick question, just plain old mathematical probability.

The answer, which I found very counter-intuitive at first, is 23. It’s called the Birthday Paradox. The mistake I was making (and that most people would probably make) is that I was picking a single birthday and thinking of the probability of any given birthday matching it rather than moving on and testing for every other birthday possibility in the group.

I still struggle with it however, when I think back to school days where there should have been a 100% chance of two kids sharing a birthday in any two classes. I can’t remember anyone sharing a birthday at all.

(Or have I done the math wrong here by assuming that two classes of 23 students will give a 100% chance? Perhaps this equates to 75% instead or remains at 50%? Gaaah! I knew I should have listened in school!).

Jack, if you are reading this perhaps you could test this to see if it really works in a class situation?