If 2 different representatives are to be selected at random

Question

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.

Stay tuned for the OA :wink:

KillerSquirrel · Answer

this answer was deleted ! to avoid confusion ! see the right answer in the followup posts. :oops:

Himalayan · Answer

10c2 = 45 we need total 23 pairs of women to have p>1/2 to have 23 pair, we need 8 women. from 1: if w = 6, 6c2 = 15, p = 15/45 <1> 1/2 so nsf. from 2: if p < 1/10 for both men, no of pair of both men is less than 4.5. since 4.5 pair can not be possible therefore it must be 4 or 3 or 2 or 1. what ever be the pair, no of men can not be more than 3 because if no of men is 4, then the pair of both men becomes 6, which is not possible.. therefore the no of men is 3 or less than 3. if n (men) = 3......p (both women) <1> 1/2 so still not suff..... togather is also nsf.

Himalayan · Answer

this is not what i have posted. i tried reposting what i did but it is not posting what exactly i wrote.

10c2 = 45

we need total 23 pairs of women to have p > 1/2
to have 23 pair, we need 8 women.

from 1:

if w = 6, 6c2 = 15, p = 15/45 is less 1/2
if w = 7, 7c2 = 21, p = 21/45 is less 1/2
if w = 8, 8c2 = 28, p = 28/45 is grater 1/2

so nsf.

from 2:
if p < 1/10 for both men, no of pair of both men is less than 4.5. since 4.5 pair can not be possible therefore it must be 4 or 3 or 2 or 1. what ever be the pair, no of men can not be more than 3 because if no of men is 4, then the pair of both men becomes 6, which is not possible.. therefore the no of men is 3 or less than 3. 

if m = 3, w = 7, 7c2 = 21, p = 21/45 is less 1/2

if m = 2, w = 8, 8c2 = 28, p = 28/45 is grater 1/2

so still not suff.....

togather is also nsf.


EEE

vikramjit_01 · Answer

Nice work Himalayan (nice avatar too) especially with Statement II. Both statements almost reach the same conclusion from opposite directions and so C doesn't stand a chance here. Yes OA = E :good

Himalayan · Answer

Thanks Vikramjit. my avatar is a real picture of KUMARI, a living goddes. more about Kumari: https://en.wikipedia.org/wiki/Kumari

vikramjit_01 · Answer

From that link "The power of the Kumari is perceived to be so strong that even a glimpse of her is believed to bring good fortune" I guess Himalayan's avatar might bring us all some good fortune

Himalayan · Answer

Fortunately, I had her glimpses. She is above beauty (800). :wink:

If 2 different representatives are to be selected at random

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards