SOLUTION: In the game of tennis, first serves are distinct from second serves in that the player will generaly take a more powerful swing (bigger chance for error) on the first serve, since

Question 1114823: In the game of tennis, first serves are distinct from second serves in that the player will generaly take a more powerful swing (bigger chance for error) on the first serve, since he/she is always allowed a second serve if the first lands out of bounds. Suppose a tennis player makes a successful first serve 46% of the time, and she will serve 20 first serves in a row.
a. If we assume that each serve is independent of the others, why does the number of successful first serves follow a binomial process? Justify your answer.
b. Let X = the number of successful first serves. Write a probability that she makes at least 7 successful first serves in terms of X, and find the probability.
c. What is this players average number of first serves in, if she served many sets of 20 first serves?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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
:
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)!)
:
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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