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Part (a): The possible outcomes are listed below, organized by who wins the match. Within each match winner category, who wins each set is shown. 1) 11) Player V wins: vv VMV MVV Player M wins. MM MVM VMM Part (b): The ways in which Player V can win a match against Player M and the corresponding probabilities are shown below. Adding the probabilities for the various ways Player V wins the match yields the overall probability of 0.4575. Outcome VV VMV MVV Probability (0.5)(0.6)=0.3 (0.5)(1 -0.6) (0.45) = 0.09 (0.5)(1 0.7)(0.45) = 0.0675 Total: 0.3 + 0.09 +0.0675 = 0.4575 Part (c): P(3 sets | V wins) = P(3 sets and V wins) (0.09 +0.0675) P(V wins) 0.4575 0.1575 ≈ 0.344 0.4575 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. What is the probability that a match between Player V and Player M will consist of 3 sets given that Player V wins the match?

Part (a): The possible outcomes are listed below, organized by who wins the match. Within each match winner category, who wins each set is shown. 1) 11) Player V wins: vv VMV MVV Player M wins. MM MVM VMM Part (b): The ways in which Player V can win a match against Player M and the corresponding probabilities are shown below. Adding the probabilities for the various ways Player V wins the match yields the overall probability of 0.4575. Outcome VV VMV MVV Probability (0.5)(0.6)=0.3 (0.5)(1 -0.6) (0.45) = 0.09 (0.5)(1 0.7)(0.45) = 0.0675 Total: 0.3 + 0.09 +0.0675 = 0.4575 Part (c): P(3 sets | V wins) = P(3 sets and V wins) (0.09 +0.0675) P(V wins) 0.4575 0.1575 ≈ 0.344 0.4575 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. What is the probability that a match between Player V and Player M will consist of 3 sets given that Player V wins the match?

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.2: Introduction To Probability
Problem 32E
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Why P(3 sets and V wins) = (0.09+0.0675)? The formula for the probability of the intersection of two events A and B is P(A) * P(B). But, why did we add (0.09+0.0675)?

Part (a): The possible outcomes are listed below, organized by who wins the match. Within each match winner category, who wins each set is shown. 1) 11) Player V wins: vv VMV MVV Player M wins. MM MVM VMM Part (b): The ways in which Player V can win a match against Player M and the corresponding probabilities are shown below. Adding the probabilities for the various ways Player V wins the match yields the overall probability of 0.4575. Outcome VV VMV MVV Probability (0.5)(0.6)=0.3 (0.5)(1 -0.6) (0.45) = 0.09 (0.5)(1 0.7)(0.45) = 0.0675 Total: 0.3 + 0.09 +0.0675 = 0.4575 Part (c): P(3 sets | V wins) = P(3 sets and V wins) (0.09 +0.0675) P(V wins) 0.4575 0.1575 ≈ 0.344 0.4575
Transcribed Image Text:Part (a): The possible outcomes are listed below, organized by who wins the match. Within each match winner category, who wins each set is shown. 1) 11) Player V wins: vv VMV MVV Player M wins. MM MVM VMM Part (b): The ways in which Player V can win a match against Player M and the corresponding probabilities are shown below. Adding the probabilities for the various ways Player V wins the match yields the overall probability of 0.4575. Outcome VV VMV MVV Probability (0.5)(0.6)=0.3 (0.5)(1 -0.6) (0.45) = 0.09 (0.5)(1 0.7)(0.45) = 0.0675 Total: 0.3 + 0.09 +0.0675 = 0.4575 Part (c): P(3 sets | V wins) = P(3 sets and V wins) (0.09 +0.0675) P(V wins) 0.4575 0.1575 ≈ 0.344 0.4575
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. What is the probability that a match between Player V and Player M will consist of 3 sets given that Player V wins the match?
Transcribed Image Text: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. What is the probability that a match between Player V and Player M will consist of 3 sets given that Player V wins the match?
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