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Probability problem - please help with solution

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by shakes_d82 » Wed Oct 24, 2012 6:31 am
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.
[A] Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
[C] BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
[D] EACH statement ALONE is sufficient.
[E] Statements (1) and (2) TOGETHER are NOT sufficient.
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Source: — Data Sufficiency |
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by anuprajan5 » Wed Oct 24, 2012 6:50 am
The answer is A

Statement 1 - More than 1/2 of the 10 employees are women.

This means there are atleast 6 women and 4 men and atmost 9 women and 1 man

Taking the first case p(both women) = 6/10*5/9 = 1/3
Taking 2nd case p(both women) = 9/10*8/9 = 8/10

In both cases p>1/2. Sufficient.

STatement 2 - I can't solve this one because we don't know the man/woman split and we can't take the reverse approach of 1-(p both men) because that answer would have the probability of 1 man and 1 woman also in it. Insufficient.

REgards
Anup
Regards
Anup

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