The complement event would be for all 30 students to have
all different birthdays.  There are 365P30 ways to assign
them all different birthdays and 36530 ways to assign
then any birthdays.  So the probability of all 30 having
different birthdays is







So the probability that at least 2 students have the same birthday is
that number subtracted from 1, which is:



or about a 71% probability that at least 2 students among the 30
have the same birthday.

Edwin