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Get Full Access to Elementary Statistics - 12 Edition - Chapter 5.5 - Problem 3cre
Get Full Access to Elementary Statistics - 12 Edition - Chapter 5.5 - Problem 3cre

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# Tennis Challenge In the last U.S. Open tennis tournament, ISBN: 9780321836960 18

## Solution for problem 3CRE Chapter 5.5

Elementary Statistics | 12th Edition

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Problem 3CRE

Problem 3CRE

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.

Step-by-Step Solution:

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 172 439 611

1. If one of the 611 challenges is randomly selected, we have to find the probability that it resulted in an overturned call.

There are 172 challenge upheld with overturned call

The total of challenges is 611.

Therefor,

the probability that it upheld with overturned call  = 172/611 = 0.2815

b) If one of the challenges made by the men is randomly selected, we have to find  the probability that it resulted in an overturned call.

Challenge Upheld with Overturned Call made by men = 121

The total of challenges is 611

Therefore,

the probability that it resulted in an overturned call = 121/611 = 0.198

c) If one of the challenges made by the women is randomly selected, we have to find  the probability that it resulted in an overturned call.

Challenge Upheld with Overturned Call made by women = 51

The total of challenges is 611

Therefore,

the probability that it resulted in an overturned call = 51/611 = 0.0835

d) If one of the overturned calls is randomly selected, we have to find the probability that the challenge was made by a woman

There are 172 challenge upheld with overturned call

There are 51 challenges made by women that resulted in overturned.

Therefore,

the probability that the challenge was made by a woman = 51/172 = 0.2965

e) If two different challenges are randomly selected with replacement, we have to find the probability that they both resulted in an overturned call.

There are 172 challenge upheld with overturned call

The total of challenges is 611

Therefore,

the probability that they both resulted in an overturned call =  = 0.0792

f) If one of the 611 challenges is randomly selected, we have to find the probability that it was made by a man or was upheld with an overturned call

The probability that it was made by man =  = 0.655

the probability that it upheld with overturned call  = 172/611 = 0.2815

The probability that challenge was made by a man and upheld by an overturned call is 121/611 = 0.198

the probability that it was made by a man or was upheld with an overturned call = 0.655+0.2815-0.198 =  0.7385

g) If one of the challenged calls is randomly selected, we have to find the probability that it was made by a man given that the call was upheld with an overturned call.

P(A/B) = P(was made by a man / call was upheld with an overturned cal) = = = = 0.7021

Step 2 of 1