A graduate class consists of six students. What is the probability that exactly three of them are born either March, June or November?

Answer 1

Out of six students, we need exactly 3 fit the criteria of being born in 3 months out of 12, i.e. with probability p=3/12=0.25.
Since the probability is assumed constant throughout, and we know the total number of students, we can use the binomial distribution, where
n=6
x=3
p=0.25
and the probability is given by:
P(X=x)=C(n,x)p^x (1-p)^(n-x)
where C(n,x)=binomial coefficient = n!/(x!(n-x)!).

Just plug in the numbers to get your results.