If 2 different representatives are to be selected at random

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.

From 1)

Women in the group can be (6,7,8,9,10)

Let us consider the least women in the grp first i.e. 6

Now P (2 women chosen) =  (6C1 * 5C1) / 10C2   = 30/90 = 1/3

If we chose max women in group i.e 10, the required probability is 1.

Hence Insuff.

From 2)

P(2M) ‘<’ 1/10.

Hence 1/10 ‘>’ mC1 * m-1C1 / 10C2

i.e. m^2 -1 ‘<’ 9

m^2 ‘<’10

i.e Number of Males can be (3,2) and Women can be (7,8) respectively.

If W are 7, then P(2W) = 7*6/90 = 42/90 which is less that 45/90 i.e. ½

Hence Insuff.

Ans : E.