5. Consider a group of 6 people that consists of 4 men and 2 women. a) If a subg

Question

5. Consider a group of 6 people that consists of 4 men and 2 women. a) If a subgroup of 3 of these people is selected at random, what is the probability that both women are selected? Express your answer as a fraction and as adecimal. b) Now suppose that the committee consists of Mmen and 2 women, where M is a positive integer. Determine the probability that a randomly selected subgroup of 3 committee members would include 2 women, as a function of M. Simplify your answer. c) Is this an increasing or decreasing function of M? Explain why this makes sense

Explanation / Answer

a)

total = 4+2 = 6

P(both women are selected) = 2C2 * 4C1 / 6C3 = 1 *4 / 20 = 1/5

b)

M men and 2 women

P(2 women in committtee) = 3C2 * MC1 / ((M+2)C3) = 3 * M /(M+2)(M+1)(M/6)

c)

this is decreasing function , because as the numbe of men are increasing , the probability of selecting 2 women (constant) will decrease

Please rate

c)

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