If 2 different representatives are to be selected at random fro a group of 10 employees and if p is the probability that both representatives selected will be women, is p>1/2?
(1) More than 1/2 of the 10 employees are women.
(2) The probability that both representatives selected will be men is less than 1/10.
I chose B ? The answer that I found is E ! Why? Please, Help!
(1) is obviously not sufficient.
(2) needs some computation.
Suppose that there are x men, then Prob(2 men selected)=(x/10)*((x-1)/9)<1/10. Solving the inequality involves an estimation of sqrt(37), which is close to 6. Therefore integer x must be <=3.
If x=3, then there are 7 women. Prob(2 women selected)=(7/10)*(6/9)=14/30<15/30=1/2. If x=1 or 2, Prob(2 women selected)>1/2. So (2) is not sufficient, either.
There are at least 7 women already, so (1) and (2) together are not sufficient.
Choose E.
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