Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

4

This post received KUDOS

7

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

65% (hard)

Question Stats:

57% (03:03) correct
43% (01:55) wrong based on 163 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

7

This post received KUDOS

1

This post was BOOKMARKED

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

This post received KUDOS

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 _________________

Re: If a jury of 12 people is to be selected randomly from a [#permalink]
10 Feb 2014, 17:12

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Re: If a jury of 12 people is to be selected randomly from a [#permalink]
03 Aug 2014, 16:19

Hi,

Can someone explain why my method below is incorrect?

I tried to approach it with the "1-x" method and therefore, I did a very simple calc of:

1-(5/12) where the (5/12) is the probability of choosing 5 women, therefore, only 7 men. Why is that incorrect? Why do we need to apply the combination method here and not simple probability?

Re: If a jury of 12 people is to be selected randomly from a [#permalink]
03 Aug 2014, 19:33

1

This post received KUDOS

@ russ9 : your method is incorrect,

if there are 7 men and 5 women, and we are asked to chose 1 person, then the probability of that 'one person' being a woman is 5/12. this is simple probability...

in this case we are not choosing one person, we are actually choosing 12 people, from a pool of 15 people, comprising of both men and women. So what we are trying to find is when selecting 12 people, how many combinations of those 12 people would contain 5 women? thats what we trying to find out.. that why we use combinations and not simple probability.

Hope its clear

gmatclubot

Re: If a jury of 12 people is to be selected randomly from a
[#permalink]
03 Aug 2014, 19:33

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...