Adam and Eve are in a room with $n − 2$ other people. Suppose you know that at least two of the people in the room celebrate their birthday on the same day. What is the probability that Adam and Eve celebrate their birthday on the same day? (Assume that a year has 365 days and that the distribution of births over a year is uniform.)
I think it is knowing that at least two people have the same birthday that is confusing to me. Does it change anything to have this info?