In the last U.S. Open tennis tournament, there were 611 challenges made by singl

Question

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. 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 challenges made by the men is randomly selected, what is the probability that it resulted in an overturned call? c. If two different challenges are randomly selected with replacement, find the probability that they both resulted in an overturned call. d. 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. e. 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.

Explanation / Answer

a) 172 out of 611 referee calls were overturned, P(referee call overturned) = 172/611 = 0.2815

b) 121 out of 121+279 = 400, referee calls were overturned for men,
P(referee call overturned for men) = 121/400 = 0.3025

c) P(2 calls overturned with replacement) = 0.2815*0.2815 = 0.07924

d) P(man union overturned) = P(man & overturned) + P(man & no change) + P(female & overturned)
= 121/611 + 279/611 + 51/611 = 0.7381

e) P(Man|overturned) = P(man and overturned)/P(overturned) = (121/611)/(172/611) = 0.7035

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