Find the smallest number of people you need to choose at random so that the probability that at least one has a birthday today exceeds 1/2.
About all I have so far is that (assuming a 365 day calendar year), the probability of a person having a birthday today is 1/365 and the probability of the opposite is 364/365. Where do I go from here?
HINT: Suppose you choose $n$ people. If each person has probability $1-p$ of failing to have a birthday today, what is the probability that all $n$ people fail to have a birthday today?