Tree Diagrams 4 P Take a Test cynthia Davis Google Chrome h

Tree Diagrams - 4

P Take a Test cynthia Davis Google Chrome https:// 110724450&centerwin; yes Cynthia Davis 12/8/15 11:22 AM Quiz: 6.5 (quiz) Tree Diagrams Overview 1 2 3 4 5 6 90 10 This Question: 1 pt This Test: 10 pts 0 of 10 Kim has a strong first serve, whenever it is good that is, in) she wins the point 85 of the time. Whenever her second serve is good, she wins the point 60% of the time. Seventy percent of her first serves and 90% 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 Vi Vi (a The probability that Kim wins the point when she serves is OUT Lose Type an integer or a decimal.) OUT Win (b The probability that Kim\'s first serve is good if she wins the service Lose point is Type an integer or a decimal rounded to the nearest hundredth as Win needed. Lose Enter your answer in each of the answer boxes. I Previous Question Next Question Submit Quiz

Solution

NOTE: 2nd serve come into picture only if 1st serve is not good .

P(1st serve good & wins point) = 0.70 * 0.85 = 0.595 = Event A

P(2nd serve good & wins point) = 0.3 * 0.9 *0.6 = 0.162 = Event B

a)

P(Win point) = Event A+Event B = Event C = 0.595 + 0.162 = 0.76 Answer

b)

P(1st serve good | win point )= A/C = 0.595 / 0.757 = 0.79 Answer