A pool of 10 semifinalists for a job consists of 8 men and 2 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,) = | % and P(W, | W,) = %, and thus P(W, n W2) = P(W2 I W;) P(W;) = %. Hence, the probability that both finalists are women is %. (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? %
A pool of 10 semifinalists for a job consists of 8 men and 2 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,) = | % and P(W, | W,) = %, and thus P(W, n W2) = P(W2 I W;) P(W;) = %. Hence, the probability that both finalists are women is %. (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? %
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:A pool of 10 semifinalists for a job consists of 8 men and 2 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,)
% and P(W2 | W1) =
%, and thus
P(W, n W2) = P(W, I W;) P(W,) =
%.
Hence, the probability that both finalists are women is
%.
(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?
%
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