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A pool of 10 semifinalists for a job consists of 6 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) = 40 % and P(W₂ | W₁) = 33.3 Hence, the probability that both finalists are women is (b) What is the probability (as a %) that both finalists are men? X % (c) What is the probability (as a %) that one finalist is a woman and the other is a man? X% Need Help? %. Read It %, and thus P(W₁ W₂) = P(W₂ | W₁) P(W₁) = 13.3 ✓ %.

A pool of 10 semifinalists for a job consists of 6 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) = 40 % and P(W₂ | W₁) = 33.3 Hence, the probability that both finalists are women is (b) What is the probability (as a %) that both finalists are men? X % (c) What is the probability (as a %) that one finalist is a woman and the other is a man? X% Need Help? %. Read It %, and thus P(W₁ W₂) = P(W₂ | W₁) P(W₁) = 13.3 ✓ %.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A pool of 10 semifinalists for a job consists of 6 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? 1 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. 2 Then, as percents, P(W₁) = 40 % and P(W₂ | W₁) = 33.3 Hence, the probability that both finalists are women is (b) What is the probability (as a %) that both finalists are men? X % (c) What is the probability (as a %) that one finalist is a woman and the other is a man? X % Need Help? X %. Read It %, and thus P(W₁ W₂) = P(W₂ | W₁) P(W₁) = 13.3 %.
Transcribed Image Text:A pool of 10 semifinalists for a job consists of 6 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? 1 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. 2 Then, as percents, P(W₁) = 40 % and P(W₂ | W₁) = 33.3 Hence, the probability that both finalists are women is (b) What is the probability (as a %) that both finalists are men? X % (c) What is the probability (as a %) that one finalist is a woman and the other is a man? X % Need Help? X %. Read It %, and thus P(W₁ W₂) = P(W₂ | W₁) P(W₁) = 13.3 %.
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