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Birthday Problem (Classic)

A classic problem.

How many people do you need to have in a room so that the probability of at least 2 of people sharing a birthday is greater than 50%.

Assume 365 days in a year (no leap years), and birthdays are random over these 365 days, and people born in different years on the same day obviously have the same birthday.

Also, no twins, twins are cheating.

The solution is easier to understand if you realize that with 23 people in the room there are 23 * 22 / 2 = 253 possible pairings.

To find the probability, first find that probability that n number of people don’t share a birthday. The equation for this is

p(n) = 1 x (1 – 1/365) x (1 – 2/365) x …. x (1 – (n – 1)/365)

The probability that any 2 do share a birthday is then 1 – p(n). Doing the math we find that at 23 people the probability that at least 2 of them share the same birthday is 50.7%.

Comments


sincerekamal

confusing... :(


Vishal barot

If you dont understand then goto
http://www.mathsisfun.com/data/probability-shared-birthday.html


Gene

I saw a fellow telling Johnny Carson about this problem on the Tonight Show many years ago. Carson looked incredulous and then asked the audience, "Does anybody here have a birthday on..." and then said his birthday. When no one answered, he looked at the guy like he was nuts. It may have been that someone did have the same birthday as Carson but didn't speak up. But even if he had, that wasn't what the guest had said. For a 50% likelihood of someone having a GIVEN birthday, you need about 183 people. But for a 50% likelihood of ANY TWO people in a group having the SAME birthday, you need only 23 people.


ylq

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