SOLUTION: This is known as the Birthday Problem. (a) Consider a class with 30 students. Compute the probability that at least two of them have their birthdays on the same day. (For simplic

Algebra ->  Probability-and-statistics -> SOLUTION: This is known as the Birthday Problem. (a) Consider a class with 30 students. Compute the probability that at least two of them have their birthdays on the same day. (For simplic      Log On


   

Question 1051953: This is known as the Birthday Problem.
(a) Consider a class with 30 students. Compute the probability that at least two of them
have their birthdays on the same day. (For simplicity, ignore the leap year).
(b) How many students should be in class in order to have this probability above 0.5?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

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

%22%22=%22%22

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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