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.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.