If there are 23 people in a room, the mathematical chances that 2 of them have the same birthdate are better than 50/50. And if you have 57 people or more in a room, the odds are 99% and above that 2 of them have the same birthday.
Doubt it? The reason that this seems strange or even ridiculous, is because of how we are used to doing comparisons. In this case, we probably think like this--
ďOkay then, letís take one person in the room, letís say Jane. Now if I go around to each other person in the room, and ask what that personís birthday is and then compare it to see if itís the same as Janeís birthday, then the chances that that one personís birthday is the same as Janeís are 1 out of 365. So realizing that there are 22 other people, not just 1, then the chances that Iíll find someone matching Janeís birthday are 22 out of 365.Ē
Now donít get me wrong, that is true, but that is NOT the same thing as the original statement laid down. And therein lies the catch.
Admittedly, if you try to compare 22 birthdays to ONE SPECIFIC birthday, you come out with the numbers above. But we are not talking about comparing 1 specific birthday to 22 other birthdays. We are talking about comparing ANY ONE of a group of 23 birthdays to each one of the other 22 birthdays to find a match. Now THAT is a different thing, and the math of doing it is hugely detailed from what I hear.
But the result of the detailed math is the 50/50 thing with 23 people as stated above, and approaching very close to 100% certainty if more than about 50 people are in the room.