Math

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If the probability that a certain tennis player will serve an ace is 1/4, what is the probability that he will serve exactly two aces out of four serves? (Assume that the four serves are independent. Round your answer to four decimal places.)

  • Math -

    I guess I will have to use binomial coefficients.

    the probability of k successes in n trials is:

    P(k) = C(n,k) p^k (1-p)^(n-k)
    C(n,k) is binomial coef
    get from Pascal triangle or table or calculate from
    C(n,k) - n! / [ k! (n-k)! ]

    here
    p = prob of ace = .25
    (1-p) = .75
    n = 4
    k = 2

    C(4,2) = 4! /[2!(2!)] = 4*3*2/[2(2)] = 6
    so
    P(2) = 6 (.25)^2 (.75)^2
    = .21

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