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If 2 different representatives are to be selected at random from a group

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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 > 21 ?. 
(1) More than! of the 10 employees are women. 
(2) The probability that both representatives selected will be men is less than 11.

1 Answer

flamingo
0
Let us suppose no of women to X. In that case the probability of selecting 2 woman > 0.5
X * ( X - 1 ) / 2 / ( 10 * 9 / 2) > 0.5
X * ( X - 1 ) > 45
which clearly indicates the X > 7 or in other words it would mean man should be < 3.
From the first statement : More than 1/2 of the 10 employees are woman.
but this does not help. hence insufficient.
From the second statement : Y ( Y - 1 ) / 10 * 9 < 1/10
Y(Y-1) < 9
Y can be 0,1,2,3
Combining both statements also does not solve the question.
Hence answer is E
answered Feb 25, 2015 by Guru (5,599 points)
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