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# If 2 different representatives are to be selected at random

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Manager
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If 2 different representatives are to be selected at random [#permalink]

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18 May 2007, 14:25
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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 > 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
VP
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18 May 2007, 14:31
this answer was deleted ! to avoid confusion !

see the right answer in the followup posts.

Last edited by KillerSquirrel on 18 May 2007, 15:26, edited 3 times in total.
Director
Joined: 26 Feb 2006
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18 May 2007, 14:40
vikramjit_01 wrote:
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

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.
Director
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18 May 2007, 14:50
Himalayan wrote:
vikramjit_01 wrote:
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

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.

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
Manager
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18 May 2007, 15:22
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
Director
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18 May 2007, 15:36
vikramjit_01 wrote:
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

Thanks Vikramjit. my avatar is a real picture of KUMARI, a living goddes.

Manager
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19 May 2007, 06:31
"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
Director
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19 May 2007, 10:54
vikramjit_01 wrote:
"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

Fortunately, I had her glimpses. She is above beauty (800).
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# If 2 different representatives are to be selected at random

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