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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
Solution
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.
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