Answer to Question #348724 in Statistics and Probability for Star

Question

In the class of Statistics, there are 75 students in total out of which 55 male, 20 female students. 10 students need to be selected for the occasion of freshers' reception.

a. Determine the probability that 4 of the selected students would be girls by using the formula of binomial distribution.

Answer 1

Let $X=$ the number of girls: $X\sim Bin(n, p).$

Given $n=10, p=20/75=4/15, q=1-p=11/15$

$$P(X=4)=\dbinom{10}{4}(\dfrac{4}{15})^{4}(\dfrac{11}{15})^{10-4}$$ $$\approx0.16516$$