Kim has a strong first? serve; whenever it is good? (that is,? in) she wins the
ID: 3150371 • Letter: K
Question
Kim has a strong first? serve; whenever it is good? (that is,? in) she wins the point 80?% of the time. Whenever her second serve is? good, she wins the point 60?% of the time. Fifty percent of her first serves and 85?% 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) The probability that Kim wins the point when she serves is _______
?(Type an integer or a? decimal.)
?(b) The probability that? Kim's first serve is good if she wins the service point is _____
?(Type an integer or a decimal rounded to the nearest hundredth as? needed.)
Explanation / Answer
Let
1I = 1st serve is in
2I = 2nd serve is in
W = Kim wins
a)
Hence,
P(W) = P(1I) P(W|1I) + P(1I') P(2I) P(W|2I) = 0.50*0.80 + (1-0.50)*0.85*0.60 = 0.655 [ANSWER]
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b)
Also,
P(1I|W) = P(1I) P(W|I1)/P(W) = 0.50*0.80/0.655 = 0.610687023 = 0.61 [ANSWER]
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