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.

hey! so 1 (25) out of 4 (100) is 25 so your answer is 25%. it's like quarters!