The birthday problem

David Kessler and Jeremy Schiff

This paper was never intended for publication. It deals with the famous "birthday problem": Assume there are D days in a year, and there is equal probability of being born on any particular day of the year. What is the probability that in a group of N people (with N no bigger than D) there are (at least) two with the same birthday? We wrote up this paper as supplementary reading for the students in our probability courses, but since it might be of wider interest I am posting it here too.