3 (a-g) thanks a. If one of the 611 challenges is randomly selected, what is the

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3 (a-g)
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a. If one of the 611 challenges is randomly selected, what is the probability that is resulted in an overhead 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.

Explanation / Answer

Following is the completed table:

(a)

Since out of 611 challenges, 172 are overturned so requried probability is

P(upheld) = 172/611 = 0.2815

(b)

Out of 400 challenges made by men, 121 are overturned so required probability is

P(overturned|men) = 121/400 = 0.3025

(c)

Out of 211 challenges made by women, 51 are overturned so required probability is

P(overturned | women) = 51/211 = 0.2417

(d)

Out of 172 overturned challenges, 51 are made by women so required probability is

P(women | overturned) = 51/172 = 0.2965

(e)

The requried probability is

P(both are overturened) = (172/611)*(172/611) = 0.0792

(f)

P(man)= 400/611

P(overturned) = 172/611

P(man and overturned) = 121/611

So required probability is

P(man or overturned) = P(man)+P(overturned) - P(man and overturned) = 0.7381

(g)

P(man | overturned) = 121/172 = 0.7035

Challenge Upheld with overturned call Challenge Rejected with No change Total Challenges are Men 121 279 400 Challenges are Women 51 160 211 Total 172 439 611

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