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 :
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 
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...