Question

The probability that a student is not a swimmer is 1/5 . Then the probability that out of five students, four are swimmers is

(A) `""^5C_4 (4/5)^4 1/5`

(B) `(4/5)^4 1/5

(C) `""^5C_1 1/5 (4/5)^4 `

(D) None of these

Answer 1

The repeated selection of students who are swimmers are Bernoulli trials. Let X denote the number of students, out of 5 students, who are swimmers.

Probability of students who are not swimmers, q= 1/5

`:. p = 1 - q = 1 - 1/5 = 4/5`

Clearly, X has a binomial distribution with n = 5 and p = 4/5

Therefore, the correct answer is A.