26-02-2011, 12:49
If you have not seen this question before, you will probably be surprised by the answer.
What is the minimum number of randomly selected people that you need in a room, such that there is a 50 : 50 chance that 2 of them have the same birthday?
Most people's first guess is 366 divided by 2, which is 183, but that is not even close.
Press the Spoiler button for the answer, and more details
What is the minimum number of randomly selected people that you need in a room, such that there is a 50 : 50 chance that 2 of them have the same birthday?
Most people's first guess is 366 divided by 2, which is 183, but that is not even close.
Press the Spoiler button for the answer, and more details
Spoiler: Show
If there are 2 people in the room the chance of them having different birthdays is 365/366.
For 3 people to all have different birthdays it is 365/366 x 364/366.
For 4 people it is 365/366 x 364/366 x 363/366.
When there are 23 people, the chance has reduced to
365/366 x 364/366 x 363/366 x .... etc .... x 345/366 x 344/366
The chance of them all having different birthdays is now less than 0.5, thus the chance of 2 of them having the same birthday is now greater than 0.5
The answer to the question is therefore 23
I read this in a book, and wrote a little computer program to confirm it. Results shown below
For 3 people to all have different birthdays it is 365/366 x 364/366.
For 4 people it is 365/366 x 364/366 x 363/366.
When there are 23 people, the chance has reduced to
365/366 x 364/366 x 363/366 x .... etc .... x 345/366 x 344/366
The chance of them all having different birthdays is now less than 0.5, thus the chance of 2 of them having the same birthday is now greater than 0.5
The answer to the question is therefore 23
I read this in a book, and wrote a little computer program to confirm it. Results shown below