Hey pang,
Thanks for pointing out. You are right, and the answer to the problem based on my understanding should indeed be 1 - (1 - n/365)^n.
But now I actually have doubts on my own version, because I don’t think n students in A could just take n different dates in a year. In opposite to your argument, I think each student in A, or to be more accurate, the events that B students have a match with any of the students in A are actually independent from each other.
Let’s say the probability of students named B1…Bn having a match with A1 is P. The probability of students B1…Bn having a match with A2 should also be P, no matter A1 or A2 have the same date or not. The date of A1 will have no influence on the date of A2, as we don’t care if there are matches among A students themselves or not.
Please advise, peers and mentors.