A committee has 6 members. There are 3 men and 3 women are on a committee. Beth

Question

A committee has 6 members. There are 3 men and 3 women are on a committee. Beth is one of the women. Two of the 6 people are randomly chosen to serve as officers. Answer the following questions. (Give your answers correct to three decimal places.) (a) What is the probability that both officers will be women? (b) What is the probability at least one officer will be a woman? (c) If you know that at least one of the officers is a woman, what is the conditional probability that both officers will be women? (d) If you know that Beth is one of the officers, what is the conditional probability that both officers are women?

Explanation / Answer

Answer to the question:

a. P( both women) = = COMBIN(3,2)/COMBIN(6,2) = .2

b. P( atleast 1 is women) = 1-P( no women) = 1-(3C2/6C2) = .8

c. P( given atleast one of officers is a woman, both are given) = (3C2/6C2)/.8= .25

d. P( given 1 is women, what is chance of 2nd woman) = (2C1/5C1) = 2/5 = .4

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