The Birthday Problem is a famous statistical problem that tells us that there is about a 50% chance that, out of just 23 people in a room, at least two of them will share the same birthday (month and day). How is the multiplication rule used to calculate this probability?
1 Answer
Feb 18, 2015
Actually, it is the subtraction rule that is more important here.
Let's try to work out the probability that they all have a different birthday:
First person may choose 365 days out of 365.
Second person has only 364 choices left,
Etc, etc.
So the chance that they all have different birthdays is:
Which works out to be
So the chance that there is at least one double is:
(I won quite a few bets on that, because it is really counter-intuitive)