Answer to Question #343258 in Statistics and Probability for ton

Question

Say 40% of the class is female. What is the probability that 6 of the first 10 students walking in will be female?

Answer 1

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

Given $n=10, p=0.4, q=1-p=0.6.$

$$P(X=6)=\dbinom{10}{6}(0.4)^6(0.6)^{10-6}=0.111476736$$