Probability

Question

If there are 42 students in your class, what is the probability that at least one of them shares your birthday?

Answer 1

The best way is to figure out the probability that NONE of them share you birthday, and then subtract that from 1.

 

There are 42 students, including you, so there are 41 others.  The odds that any one of them does not have the same birthday as you is 364/365.  (I'm forgetting about leap year.)  Since each person's birthday is an independent event, the odds that ALL of them don't have the same birthday as you is (364/365)⁴¹= 0.894.  So the odds that at least one of them will share your birthday is 0.106 = 10.6%.