what is a birthday paradox?

Answer 1

Generally, the formula for the probability that at least 2 people out of n share the same birthday (but not necessarily the same year of birth) is

p = 1 - 365! / ((365-n)! * 365^n).

(Of course, it assumes that there are no leap years and each person is equally likely to be born on each day of the year.)

The formula gives a value that is almost equal to 1 for e.g. n=70, which is a rather counter-intuitive result at first hearing. This is why it is named a paradox, although it is not a true paradox since it does not imply a contradiction in mathematical principles. If you can do some computer programming, you can verify the result via numerical simulation.

At the university, our tutor wanted to test the result in real life by telling us to shout our birthdays one by one and the first person who shared his/her birthday with someone was supposed to interrupt the row. The tutor started with his birthday, and someone immediately stood up saying 'I was born the same day'.

Answer 2

In probability, it's the fact that if 23 (or more) people are in a group, the probability of 2 (or more) of them having the same birth date is over 50%. They may have been born in different years, but the day and month will be the same.


Doug