Answer to Question #11283 in Statistics and Probability for omar

Question

A random sample of N people is collected. Let A be the event that, among those N people, AT LEAST two
have the same birthday (this includes the case when three people have the same birthday, and the case
when ALL of them have the same birthday, or half of them have one birthday and the other half have another
birthday, etc and numerous other cases!)

The question is: to find the smallest N so that the probability of the above event A is more than 0.5.

Assume that every person has a birthday that is equally likely to fall in any of the 365 days of the year. IGNORE leap years.

Hint: First answer the question: what is the P(A) when there are exactly N people, i.e. assume N is known first.