Question 1114823
a) either the first serve is successful(in the box) or it is not - this is binomial probability.
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b) the general form of the binomial probability formula is
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Probability (P) (k successes in n trials) = nCk * p^k * (1-p)^(n-k), where p is the probability of success, nCk = n!/(k! * (n-k)!)
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P (at least 7 successful serves out of 20) = summation of k = 7 to 20 of P(k successes in 20 trials) 20Ck * 0.46^k * (1-0.46)^(20-k) = 0.888 approximately 0.89
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c) players average is 0.46 * 20 = 9.2 approximately 9
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