A pool of 12 semifinalists for a job consists of 8 men and 4 women. Because all are considered equally qualified, the names of two of the semifinalists are drawn, one after the other, at random, to become finalists for the job. (Round your answers to one decimal place.) (a) What is the probability (as a %) that both finalists are women? Let W₁ be the event that a woman is chosen on the first draw, W₂ be the event that a woman is chosen on the second draw, M₁ be the event that a man is chosen on the first draw, and M2 be the event that a man is chosen on the second draw. Then, as percents, P(W₁) = %, and thus P(W, n W₂) = P(W₂ | W₁₂) P(W₁) = % and P(W₂ | W₁) = Hence, the probability that both finalists are women is %. %. (b) What is the probability (as a %) that both finalists are men? 42.4 % (c) What is the probability (as a %) that one finalist is a woman and the other is a man? 9.1 %

A pool of 12 semifinalists for a job consists of 8 men and 4 women. Because all are considered equally qualified, the names of two of the semifinalists are drawn, one after the other, at random, to become finalists for the job. (Round your answers to one decimal place.) (a) What is the probability (as a %) that both finalists are women? Let W₁ be the event that a woman is chosen on the first draw, W₂ be the event that a woman is chosen on the second draw, M₁ be the event that a man is chosen on the first draw, and M2 be the event that a man is chosen on the second draw. Then, as percents, P(W₁) = %, and thus P(W, n W₂) = P(W₂ | W₁₂) P(W₁) = % and P(W₂ | W₁) = Hence, the probability that both finalists are women is %. %. (b) What is the probability (as a %) that both finalists are men? 42.4 % (c) What is the probability (as a %) that one finalist is a woman and the other is a man? 9.1 %

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section: Chapter Questions

Problem 41CT: On a game show, a contestant is given the digits 3, 4, and 5 to arrange in the proper order to form...

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