Kim has a strong first​ serve; whenever it is good​ (that is,​ in) she wins the point 70​% of the time. whenever her second serve is​ good, she wins the point 40​% of the time. fifty dash five percent of her first serves and 70​% of her second serves are good. ​(a) what is the probability that kim wins the point when she​ serves? ​(b) if kim wins a service​ point, what is the probability that her 1st serve was​ good?

a) There is a 63.35% probability that Kim wins the point when she serves.

b) If Kim wins a service​ point, there is a 55.80% probability that her 1st serve was​ good.

Step-by-step explanation:

We have these following probabilities

A 50.5% probability that her first serve is good.

A 70% probability that her second serve is good.

If her first serve is good, she has a 70% probability of winning the point.

If her second serve is good, a 40% probability of winning the point.

​(a) What is the probability that Kim wins the point when she​ serves?

This is the sum of 70% of 50.5% and 40% of 70%. So

There is a 63.35% probability that Kim wins the point when she serves.

​(b) If Kim wins a service​ point, what is the probability that her 1st serve was​ good?

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

So

What is the probability of Kim's first serve being good, given that she won the point?

P(B) is the probability of Kim's first serve being good. So .

P(A/B) is the probability of Kim's winning the point when her first serve is good. So .

P(A) is the probability of Kim's winning the point. From a), that is

If Kim wins a service​ point, there is a 55.80% probability that her 1st serve was​ good.

24

step-by-step explanation:

the graph shows 30% of students walk. 80 students were questioned, so the number that said they walk is

30% × 80 = 0.30 × 80 = 24

answer: the correct answer is -32

step-by-step explanation: