Eight strangers are in a room together. What is the probability that at least two of them have the same birthday. You may assume that none of them were born on February 29th.

Question

anonymous · Answer

Do the problem in reverse; the "opposite" of at least two of them having the same birthday would be if NONE of them had the same birthday. Calculate that probability, then subtract it from 1. Keep in mind that the first person has a choice of 365/365 birthdays, but the next person has 364/365 birthday choices (can't repeat the 1st guy), the next one has 363/365 choices (can't repeat either of the other two), etc...