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The probability that a student is not a ...

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

Text Solution

Verified by Experts

The correct Answer is:
`((4)/(5))^(4)`
Let p be the probability that a student selected at rondom is a swimmer, which is given by `1-1//5=4//5.` The number of students selected is 5. Probability that exactly 4 students are swimmers is
`""^(5)C_(4)p^(4)q=5((4)/(5))^(4)((1)/(5))=((4)/(5))^(4)`
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