What are the chances that at least two out of a group of fifty people
share the same birthday?
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?
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6 comments:
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.
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%
1- (365/365)*(364/365) ...... (316/365)
It would come around 97%.......
Its really High....
@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!
@Secret Squirrel - You are correct. I didn't multiply the individual probabilities prior to taking the 1-product.
Great brain teaser!
100%
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