There are two questions about the probability of shared birthdays in a group of people: 1) With a normal 365 day year, the probability is greater than 50% that two people will share a birthday when there are 23 or more people in the room. 2) Assuming N days in a year, the number of people needed for over a 50% probability of a shared birthday is approximately the square root of 2N.

1. Week 46 (7/28/03)
The birthday problem
(a) How many people must be in a room in order for the probability to be greater
than 1/2 that at least two of them have the same birthday? (By “same birth-
day”, we mean the same day of the year; the year may differ.) Ignore leap
years.
(b) Assume there is some large number, N, of days in a year. How many people
are now necessary for the odds to favor a common birthday? Equivalently,
assuming a normal 365-day year, how many people are required for the prob-
ability to be greater than 1/2 that at least two of them were born in the same
hour on the same date? Or in the same minute of the same hour on the same
date? Neglect terms in your answer that are of subleading order in N.