In women’s tennis, a player must win 2 out of 3 sets to win a match. If a player wins the first 2 sets, she wins the match and the third set is not played. Player V and Player M will compete in a match. Player V and Player M have competed against each other many times. Historical data show that each player is equally likely to win the first set. If Player V wins the first set, the probability that she will win the second set is 0.60. If Player V loses the first set, the probability that she will lose the second set is 0.70. If Player V wins exactly one of the first two sets, the probability that she will win the third set is 0.45.  What is the probability that Player V will win a match against Player M?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CR: Chapter Review
Problem 75E
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In women’s tennis, a player must win 2 out of 3 sets to win a match. If a player wins the first 2 sets, she wins the 
match and the third set is not played. Player V and Player M will compete in a match.

Player V and Player M have competed against each other many times. Historical data show that each player is 
equally likely to win the first set. If Player V wins the first set, the probability that she will win the second set 
is 0.60. If Player V loses the first set, the probability that she will lose the second set is 0.70. If Player V wins 
exactly one of the first two sets, the probability that she will win the third set is 0.45. 
 What is the probability that Player V will win a match against Player M?

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