For this problem, assume that there are 5 men and 8 women on the committee, and that a subcommittee of 3 is selected at random. What is the probability that all are male given that all are the same sex? Next, assume that the committee contains 5 men and 9 women and that three are selected at random for a subcommittee. What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter12: Probability
Section12.CR: Chapter 12 Review
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For this problem, assume that there are 5 men and 8 women on the committee, and that a subcommittee of 3 is selected at random.

What is the probability that all are male given that all are the same sex?

Next, assume that the committee contains 5 men and 9 women and that three are selected at random for a subcommittee.

What is the probability that the subcommittee consists of 2 men and 1 woman, given that it contains both men and women? 

 
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