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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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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