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# If 2 different representatives are to be selected at random

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Senior Manager
Joined: 27 Aug 2007
Posts: 253
Followers: 1

Kudos [?]: 10 [0], given: 0

If 2 different representatives are to be selected at random [#permalink]  17 Nov 2007, 05:33
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.

thank you for your help
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

Kudos [?]: 128 [0], given: 0

[#permalink]  17 Nov 2007, 06:02
p = 10

x = the number of women

n = the number of men

x/10*(x-1)/9 > 1/2 ?

statement 1

x > 5 = {6,7,8,9,10}

x = 7

7/10*6/9 = 42/90 ---> smaller then 1/2

x = 8

8/10*7/9 = 56/90 = 28/45 ---> bigger then 1/2

insufficient

statement 2

(n/10*(n-1)/9) < 1/10

possible value for n = {3,2,1,0} = possible value for x = {7,8,9,10}

insufficient

both statements

n can be 3 and x can be 7 ---> 3 men & 7 women ---> false

n can be 2 and x can be 8 ---> 2 men & 8 women ---> true

the answer is (E)

Director
Joined: 26 Feb 2006
Posts: 905
Followers: 4

Kudos [?]: 52 [0], given: 0

Re: Set #1 (if so exists) [#permalink]  18 Nov 2007, 11:45
Ferihere 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.

thank you for your help

nothing to add to KS's expert solution.
Re: Set #1 (if so exists)   [#permalink] 18 Nov 2007, 11:45
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# If 2 different representatives are to be selected at random

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