No. There's about a 22/365 chance that somebody has a birthday on that day. But this is getting close to the intuition. Go through the 23 people. For each one of them, there's about a 22/365 somebody else in the group has the same birthday as they do. So adding these probabilities up over all 23, you get 23 * 22/365. Of course, adding up the probabilities is obviously wrong since the events are not independent (and 23 * 22/365 > 1) but it gives the intuition that the probability of a shared birthday grows like N^2. [and actually, you can add up expectations] [Edits for correctness]