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If a jury of 12 people is to be selected randomly from a [#permalink]
04 Feb 2008, 15:40

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Difficulty:

55% (medium)

Question Stats:

41% (02:43) correct
58% (02:18) wrong based on 31 sessions

If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men?

Re: potential jury members [#permalink]
04 Feb 2008, 16:32

5

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We have a pool of 10 men and 5 women We need a jury of 12 people

What is the probability that the jury will comprise at least 2/3 men?

2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.

15C12 = 455 ways to select a jury of 12 from a pool of 15 5C5 = 1 way to select all 5 women 10C7 = 120 ways to select 7 men from a pool of 10 1*120 = 120 ways to select a jury with fewer than 8 men

Re: potential jury members [#permalink]
06 Feb 2008, 14:35

eschn3am wrote:

We have a pool of 10 men and 5 women We need a jury of 12 people

What is the probability that the jury will comprise at least 2/3 men?

2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.

15C12 = 455 ways to select a jury of 12 from a pool of 15 5C5 = 1 way to select all 5 women 10C7 = 120 ways to select 7 men from a pool of 10 1*120 = 120 ways to select a jury with fewer than 8 men

(455-120)/455 = 335/455 = 67/91

Answer D

clear answer, thanks - one question though, the numerator is 455-120; is that 120 because you have multiplied by the 1? i.e. if there were two ways, would it have been 120*2 leading to 455-240?

Re: potential jury members [#permalink]
06 Feb 2008, 17:54

gmatraider wrote:

eschn3am wrote:

We have a pool of 10 men and 5 women We need a jury of 12 people

What is the probability that the jury will comprise at least 2/3 men?

2/3 of a jury of 12 = 8 men. There will always be at least 8 men on the jury unless all 5 women are selected, in that case there will be 7 men and 5 women.

15C12 = 455 ways to select a jury of 12 from a pool of 15 5C5 = 1 way to select all 5 women 10C7 = 120 ways to select 7 men from a pool of 10 1*120 = 120 ways to select a jury with fewer than 8 men

(455-120)/455 = 335/455 = 67/91

Answer D

clear answer, thanks - one question though, the numerator is 455-120; is that 120 because you have multiplied by the 1? i.e. if there were two ways, would it have been 120*2 leading to 455-240?

The 120 is the number of possibilities where there are FEWER than 2/3 men on the jury. 455 is the number of possible ways to make up this jury. If there are 455 ways total, and 120 of those ways have fewer than 2/3 men...then (455-120) is the number of possible ways where the jury IS at least 2/3 men. We're looking for the probability that the jury will be at least 2/3 men so (455-120)/455 is our equation.

Re: Jury members selection- MGMAT [#permalink]
21 May 2009, 01:27

1

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Hi,

You have 10 men and 5 women in the initial jury. The question asks that you should have at least 2/3 men which means that in 12 people selected at least 8 are men.

But if you select 12 out of 15 you can do it in (15!)/(12!*3!) or 455 ways. Note that the worst option i.e. with least men is 7men 5 women which can be done in 120 ways.

All other options are OK meaning 8m 4W, 9M 3W etc.

Re: potential jury members [#permalink]
13 Jan 2011, 08:18

In is difficult to understand the question stem because of incorrect grammatical construction. The right to introduce this question must such “If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jurors’ pool consists of 2/3 men and 1/3 women, what is the probability that at least 2/3 of the jury will comprise of men?”

If the question stem were in the construction I have formulated above everybody would catch the point better. Frankly speaking it was difficult for me to recognize the pattern and to comprehend conditions of this question. I would request gmatraider to be more precise and orderly in representation of his/her questions.

Re: 700 plus level question [#permalink]
04 Aug 2011, 02:05

1

This post received KUDOS

Expert's post

ruturaj wrote:

If a jury of 12 people is to be selected randomly from a pool of 15 potential jurors, and the jury pool consists of 2/3 men and 1/3 women, what is the probability that the jury will comprise at least 2/3 men? 24/91 45/91 2/3 67/91 84/91 Please explain the steps to be followed?

Another way to approach it:

Total jurors - 15 Men = 2/3 = 10 Women = 1/3 = 5

Jurors to be selected = 12 Men - atleast 2/3 = at least 8 Women - at most 1/3 = at most 4

The number of women selected can be 5 or less than 5. Less than 5 means at most 4. So if I find the probability of selecting 5 women and subtract it from 1, we will get the probability of selecting at most 4 women (the required probability)

Total number of ways of selecting the jurors = 15C12 = 15*14*13/3! = 455

Number of ways of selecting 5 women jurors (and 7 men) = 5C5 * 10C7 = 10*9*8/3! = 120

Probability of selecting 5 women jurors = 120/455 = 24/91 Probability of selecting at most 4 women jurors = 1 - 24/91 = 67/91
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Re: If a jury of 12 people is to be selected randomly from a [#permalink]
10 Feb 2014, 17:12

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