It is believed that the probability of serving an ace in tennis on any given serve is 0.2.
If a tennis player serves 8 times, what is the probability that he makes an ace on at least 2 of the 8 serves?

49.67% probability that he makes an ace on at least 2 of the 8 serves.

Step-by-step explanation:

For each serve, there are only two possible outcomes. Either the player makes an ace, or he does not. The probability of the player making an ace in a serve is independent from other 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.

It is believed that the probability of serving an ace in tennis on any given serve is 0.2.

This means that

If a tennis player serves 8 times, what is the probability that he makes an ace on at least 2 of the 8 serves?

This is when .

We know that either he makes an ace on less than 2 serves, or he makes an ace in at least 2 of the serves. The sum of the probabilities of these events is 1. So

We want

So

In which

49.67% probability that he makes an ace on at least 2 of the 8 serves.

linear pair postulates