Respuesta :
Answer:
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
[tex]P = 0.7*(0.505) + 0.4*(0.7) = 0.6335[/tex]
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
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
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 [tex]P(B) = 0.505[/tex].
P(A/B) is the probability of Kim's winning the point when her first serve is good. So [tex]P(A/B) = 0.70[/tex].
P(A) is the probability of Kim's winning the point. From a), that is [tex]P(A) = 0.6335[/tex]
[tex]P = \frac{P(B).P(A/B)}{P(A)} = P = \frac{0.505*0.70}{0.6335} = 0.5580[/tex]
If Kim wins a service point, there is a 55.80% probability that her 1st serve was good.
