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A pool of 13 semifinalists for a job consists of 8 men and 5 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 w, be the event that a woman is chosen on the first draw, w, be the event that a woman is chosen on the second draw, M, be the event that a man is chosen on the first draw, and M, be the event that a man is chosen on the second draw. Then, as percents, P(W,) - 26 x % and P(W, I w,) = | %, and thus P(W, nw,) = P(W, I W,) P(W,) = [ Hence, the probability that both finalists are women is 25 x %. (b) What is the probability (as a %) that both finalists are men? (c) What is the probability (as a %) that one finalist is a woman and the other is a man? 51

A pool of 13 semifinalists for a job consists of 8 men and 5 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 w, be the event that a woman is chosen on the first draw, w, be the event that a woman is chosen on the second draw, M, be the event that a man is chosen on the first draw, and M, be the event that a man is chosen on the second draw. Then, as percents, P(W,) - 26 x % and P(W, I w,) = | %, and thus P(W, nw,) = P(W, I W,) P(W,) = [ Hence, the probability that both finalists are women is 25 x %. (b) What is the probability (as a %) that both finalists are men? (c) What is the probability (as a %) that one finalist is a woman and the other is a man? 51

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A pool of 13 semifinalists for a job consists of 8 men and 5 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 W, be the event that a woman is chosen on the first draw, W, be the event that a woman is chosen on the second draw, M, be the event that a man is chosen on the first draw, and M, be the event that a man is chosen on the second draw. Then, as percents, P(W,) = 26 X % and P(W, | W,) = %, and thus P(w, n w,) = P(W2 I w,) P(W,) = | %. Hence, the probability that both finalists are women is 25 X %. (b) What is the probability (as a %) that both finalists are men? % (c) What is the probability (as a %) that one finalist is a woman and the other is a man? 51 X %
Transcribed Image Text:A pool of 13 semifinalists for a job consists of 8 men and 5 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 W, be the event that a woman is chosen on the first draw, W, be the event that a woman is chosen on the second draw, M, be the event that a man is chosen on the first draw, and M, be the event that a man is chosen on the second draw. Then, as percents, P(W,) = 26 X % and P(W, | W,) = %, and thus P(w, n w,) = P(W2 I w,) P(W,) = | %. Hence, the probability that both finalists are women is 25 X %. (b) What is the probability (as a %) that both finalists are men? % (c) What is the probability (as a %) that one finalist is a woman and the other is a man? 51 X %
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