the failure rate in a statistics course is 20%. in a class of 30 students, find the probability that exactly five students will fail the course

Question

the failure rate in a statistics course is 20%. in a class of 30 students, find the probability that exactly five students will fail the course

Answer 1

This is a binomial distribution B(n,p) with parameters n = 30 and p = 1/5

 

P(X=5) = ₃₀C₅*(1/5)⁵(4/5)²⁵ 

 

           ~ 142506 * (1/3125) * (0.003777893)

 

           = 0.1723 = 17.23%