Question 253558
1.two men and three women are each waiting for a job interview there is only enough time to interview two people before lunch two people are chosen at random 
what is the probability that both people are women?
P(2 women) = 3C2/5C2 = 3/10
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what is the probability that at least one person is a women?
P(x>=1) = 1 - P(x=0)
P(at least one woman) = 1 - P(no women)
P(at least one woman) = 1 - 2C2/5C2 = 1 - 1/10 = 9/10
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which is more likely, one of people is a woman and the other is a man or both people are either men or women?
P(2 men) = 1/10
P(2 women) = 3/10
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P(one man and one woman) = 1 - [P(no man) + P(no woman)= 1 - [3/10 + 1/10]
= 1 - [4/10] = 6/10
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Ans: "one of the people is a woman and other is a man" has the higher prob.
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Cheers,
Stan H.