## December 31, 2009

### Birthday Probability Problem

What are the chances that at least two out of a group of fifty people
share the same birthday?

Secret Squïrrel said...

Surprisingly high - nearly 97.5%. It's a good party trick. If you have 30 or more people you can bet someone that there are at least 2 people with the same birthday and you'll win nearly 3 out of 4 times.

Damien said...

13.39%

The possibility of 50 people having 50 different birthdays is 317/366 or 86.61%.

The possibility of 2 out of 50 sharing a birthday is (1-.8661) or 13.39%

Varun said...

1- (365/365)*(364/365) ...... (316/365)

It would come around 97%.......

Its really High....

Secret Squïrrel said...

@Damien - in that case I'll bet you \$100 that in a random sample of 50 people, at least 2 of them will share a birthday. Since you think the chances of that being the case are less than 15%, you'd take the bet right?

I did say it was surprisingly high!

Damien said...

@Secret Squirrel - You are correct. I didn't multiply the individual probabilities prior to taking the 1-product.

Great brain teaser!

Anonymous said...

100%