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Tennis Challenge In the last U.S. Open tennis tournament,
Chapter 5, Problem 3CRE(choose chapter or problem)
Tennis Challenge In the last U.S. Open tennis tournament, there were 611 challenges made by singles players, and 172 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.
|
Challenge Upheld with Overturned Call |
Challenge Rejected with No Change |
Challenges by Men |
121 |
279 |
Challenges by Women |
51 |
160 |
a. If one of the 611 challenges is randomly selected, what is the probability that it resulted in an overturned call?
b. If one of the challenges made by the men is randomly selected, what is the probability that it resulted in an overturned call?
c. If one of the challenges made by the women is randomly selected, what is the probability that it resulted in an overturned call?
d. If one of the overturned calls is randomly selected, what is the probability that the challenge was made by a woman?
e. If two different challenges are randomly selected with replacement, find the probability that they both resulted in an overturned call.
f. If one of the 611 challenges is randomly selected, find the probability that it was made by a man or was upheld with an overturned call.
g. If one of the challenged calls is randomly selected, find the probability that it was made by a man given that the call was upheld with an overturned call.
Questions & Answers
QUESTION:
Tennis Challenge In the last U.S. Open tennis tournament, there were 611 challenges made by singles players, and 172 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.
|
Challenge Upheld with Overturned Call |
Challenge Rejected with No Change |
Challenges by Men |
121 |
279 |
Challenges by Women |
51 |
160 |
a. If one of the 611 challenges is randomly selected, what is the probability that it resulted in an overturned call?
b. If one of the challenges made by the men is randomly selected, what is the probability that it resulted in an overturned call?
c. If one of the challenges made by the women is randomly selected, what is the probability that it resulted in an overturned call?
d. If one of the overturned calls is randomly selected, what is the probability that the challenge was made by a woman?
e. If two different challenges are randomly selected with replacement, find the probability that they both resulted in an overturned call.
f. If one of the 611 challenges is randomly selected, find the probability that it was made by a man or was upheld with an overturned call.
g. If one of the challenged calls is randomly selected, find the probability that it was made by a man given that the call was upheld with an overturned call.
ANSWER:Answer :
Step 1 :
Given, In the last U.S. Open tennis tournament, there were 611 challenges made by singles players, and 172 of them resulted in referee calls that were overturned. The accompanying table lists the results by gender.
|
Challenge Upheld with Overturned Call |
Challenge Rejected with No Change |
Total |
Challenges by Men |
121 |
279 |
400 |
Challenges by Women |
51 |
160 |
211 |
Total |
172 |
439 |