MATHEMATICS 29

MATHEMATICAL FACTS

. Birthday Paradox

The birthday paradox says that if there are 23 people in a room, there is a more than 50% chance that two people have the same birthday. It seems counterintuitive because the probability of having a birthday on any particular day is only 1/365.

But the difference relies on the fact that we only need two people to have the same birthday as each other. If, instead, the game was to get someone with a birthday on a particular day, such as March 14, then with 23 people, there is only a 6.12% chance that someone will have that birthday.

In other words, if there are 23 people in a room, and you choose one person X, and ask, “Does anyone else have the same birthday as X,” the answer will probably be no. But then repeating this on the other 22 people increases the probability every time, resulting in a net probability of more than 50% (50.7% to be more precise).