A tennis player makes a successful first serve 65% of the time.If she serves 90 times in a match,what is the probability that she makes no more than 50 first serves? Assume that each serve is independent of the others.
A)0.337
B)0.970
C)0.018
D)0.030
E)0.663

Question

Quizplus · Accepted Answer

This problem can be solved by using the binomial distribution formula.

Let "X" be the number of successful first serves made. Then, X follows a binomial distribution with n=90 and p=0.65.

We need to find the probability that she makes no more than 50 first serves. This can be expressed as P(X≤50).

Using the binomial distribution formula, we get:

P(X≤50) = Σ_(k=0)^50 (90 C k) (0.65)^k (0.35)^(90-k)

Using a binomial probability table or a calculator, we can find that P(X≤50) ≈ 0.030.

Therefore, the best choice is D) 0.030, which is the probability that the tennis player makes no more than 50 first serves.

A Tennis Player Makes a Successful First Serve 65% of the Time.If