A tennis player makes a successful first serve 51% of the time. If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in? Assume that each serve is independent of the others

15.42% probability that she gets exactly 3 successful first serves in

Step-by-step explanation:

For each first serve there are only two possible outcomes. Either it is successful, or it is not. The probability of a first serve being successful is independent of other first serves. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

In which is the number of different combinations of x objects from a set of n elements, given by the following formula.

And p is the probability of X happening.

A tennis player makes a successful first serve 51% of the time

This means that

If she serves 9 times, what is the probability that she gets exactly 3 successful first serves in?

This is when

So

15.42% probability that she gets exactly 3 successful first serves in

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