Question 240261: I have an idea where to start but would appreciate any guidance you can provide.
Four hundred people apply for three jobs. 110 of the applicants are women.
a) If three persons are selected at random, what is the probability that all are women? (Round the answer to six decimal places.)
(b) If three persons are selected at random, what is the probability that two are women? (Round the answer to six decimal places.)
(c) If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)
(d) If three persons are selected at random, what is the probability that none is a woman? (Round the answer to six decimal places.)
(e) If you were an applicant, and the three selected people were not of your gender, should the above probabilities have an impact on your situation? Why?
(Yes),the probabilities indicate the presence of gender discrimination.
(No),because in the hiring process all outcomes are not equally likely.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Four hundred people apply for three jobs. 110 of the applicants are women.
a) If three persons are selected at random, what is the probability that all are women? (Round the answer to six decimal places.)
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ways to pick 3 women: 110C3
ways to pick 3 persons: 400C3
Prob. = 110C3/400C3 = 215820/10586800 = 0.020386..
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(b) If three persons are selected at random, what is the probability that two are women? (Round the answer to six decimal places.)
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Binomial with n = 3, p= 110/400, x=2
Ans: 3C2(110/400)^2(290/400) or binompdf(3,110/400,2) = 0.164484...
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(c) If three persons are selected at random, what is the probability that one is a woman? (Round the answer to six decimal places.)
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Comment: Same process as "b".
Ans binompdf(3,110/400,1)= 0.433641..
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(d) If three persons are selected at random, what is the probability that none is a woman? (Round the answer to six decimal places.)
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Same as "b" and "c" with x = 0
Ans: 0.381078...
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(e) If you were an applicant, and the three selected people were not of your gender, should the above probabilities have an impact on your situation? Why?
(Yes),the probabilities indicate the presence of gender discrimination.
(No),because in the hiring process all outcomes are not equally likely.
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I'll leave that for you to decide.
Cheers,
Stan H.
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