Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.

share|cite|improve this question
up vote 1 down vote accepted

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 $99.998\%$.

share|cite|improve this answer
That makes sense, thank you! – pepperjack May 4 '13 at 6:25

Hint: your approach is a good one. What is the chance if there are only two people? Three?

share|cite|improve this answer
I did not get the question sorry! only 2 people in total? – pepperjack May 4 '13 at 5:18
@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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.