# At least two people have the same birthday

If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday?

I tried solving it by taking into account the fact that it will be extremely difficult to solve for the probability of at least having the same birthday and started off by solving it in the complement fashion, where P(at least two people having the same birthday) = 1 - P(every person's birthday is unique), but have been trying to the possible numerator/denominator for this problem.

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You can read all about this famous problem here to learn how to calculate the probability that at least two of $n$ people share a birthday. In your case at least two of $85$ people will share a birthday with a probability of approximately $99.998\%$.
@pepperjack: I was trying to get you thinking down the line that the chance of a match with only two people is $1-\frac{364}{365}$, the chance of a match with three is $1-\frac {364\cdot 363}{365^2}$ and so on. It is in the link from Jared. – Ross Millikan May 4 '13 at 14:15