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The probability that a student is not a swimmer is 1 5 . The probability that out of 5 students selected at random 4 are swimmers is

Options

  1. A( 4 5 )^4
  2. B( 4 5 )^4 ( 1 5 )
  3. C( 4 5 )^5 1 5
  4. D( 4 5 )^3 1 5^2

Correct answer

A. ( 4 5 )^4

Step-by-step solution

The probability that a student is not a swimmer is P(S') = 1 5 , so the probability a student is a swimmer is P(S) = 1 - 1 5 = 4 5 . We seek the probability that exactly 4 out of 5 randomly selected students are swimmers, a binomial scenario with n=5 , k=4 , p = 4 5 , and q = 1 5 . The binomial probability formula gives P(X=4) = C(5, 4) ( 4 5 )^4 ( 1 5 )^1 . Since C(5,4) = 5 , this simplifies to 5 4^4 5^4 1 5 = 4^4 5^4 = ( 4 5 )^4 . This matches option A , so the answer is A .

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