If 2 different representatives are to be selected at random from 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.
The following cases satisfy both statements.
7 women, 3 men:
Statement 1: more than 1/2 the employees are women.
Statement 2: P(MM) = 3/10 * 2/9 = 1/15, which is less than 1/10.
Here, P(WW) = 7/10 * 6/9 = 7/15, so p<1/2.
10 women, 0 men:
Statement 1: more than 1/2 the employees are women.
Statement 2: P(MM) = 0.
Here, P(WW) = 1, so p>1/2.
Since p< 1/2 in the first case and p>1/2 in the second case, the two statements combined are INSUFFICIENT.
The correct answer is
E.
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