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