This statistics question is my favorite.But the Birthday Paradox is up there too.

Probably because it is a bit counter-intuitive.

The Birthday Paradox goes like this:

“How many random people do you need in a group before you can be nearly certain two of them will share a birthday?”

The answer is (about) 50.

With any group of 50 random people, you can be 97% certain at least 2 people in that group will share a birthday.

The numbers obviously change as the size of the crowd changes.

For instance:

Crowd Size          Probability 2 Share a Birthday

     70                              99.9%

Isn’t that crazy?

You would think it would be more.

I mean 40 people get together and there is almost a 90% chance two of them were born on the same day?!

The reason has to do with the fact that it is not the chance of one person having the same birthday as one other person.  Rather, it is the chance any two have the same birthday.

So with a group of 50 people, there are 1,275 distinct chances of a birthday match.

(49 + 48 + 47 + … + 1 = 1,275)

Look at the Wikipedia page linked above for more information on the math.

You can even worry about the proof if you wish.

Math or not, you can still enjoy the trivia of it all.