Answer to Question #110633 in Statistics and Probability for Charlotte

Question

If 3 out 10 students are female, what is the probability of finding 14 females in a class of 20 students?

Answer 1

If there are 3 female students out of 10, the probability of a student being female 0.3.

This is a binomial distribution case.

P(X =x) =${n \choose x } p^x(1-p)^{n-x}$

Let x be the event that a student is female.

n=20, x=14, p=0.3

P(X=14)=${20 \choose 14}*0.3^{14}*(1-0.3)^6$

=0.0002181