No, the birthday problem still works if you consider that the probability of being born on a particular day is uniform. It's related to the fact that the proba

No, the birthday problem still works if you consider that the probability of being born on a particular day is uniform. It's related to the fact that the probability of two people in a room having a birthday is more closely related to the number of pairs of people in the room (which in turn grows as O(n^2)), than to the number of people in the room. A detailed proof/explanation can be looked up easily with Google, if you have a bit of mathematical maturity.