Combinations

Expert replies

Jinglander: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Thu Jul 22, 2010 5:40 pm; Thanked: 1 times

by Jinglander » Sun Aug 08, 2010 2:18 pm

Hey guys sorry I dont have an answer for this

A jury of 12 is to be selected from a pool of 15. 2/3 are male 1/3 are female. What is the probability that the selected jury will be 2/3 male

Like this post

Source: Beat The GMAT — Problem Solving | Sun Aug 08, 2010 2:18 pm

indiantiger: Master | Next Rank: 500 Posts; Posts: 362; Joined: Fri Oct 02, 2009 4:18 amFollowed by: 1 member; Thanked: 26 times

by indiantiger » Sun Aug 08, 2010 2:40 pm

I think the right question is :

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?

Solution for this one is

12 people jury out of 15 so the total ways to select a jury = 15C12 = 91 * 5

2/3 men of 15 = 10
women = 5

2/3 of the jury is to be men = 8 men in the jury

question asks about atleast 8 men in the jury
so we will consider less then 8 that is 7 in order to get atleast 8 men on the jury

cases of having 7 men on the jury = 10C7 = 120

probability of having 7 men on jury = 120/(5 * 91) = 24/91 ---- (p7)

probability to have 8 men atleast = 1 - p7
1- 24/91 = 67/91

"Single Malt is better than Blended"

Like this post

Jinglander: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Thu Jul 22, 2010 5:40 pm; Thanked: 1 times

by Jinglander » Sun Aug 08, 2010 2:58 pm

Could have you done this without using the 7 and using the 8 men instead and not do 1-p7

Like this post

GMAT/MBA Expert

Rahul@gurome: GMAT Instructor; Posts: 1179; Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members; Location: Milpitas, CA; Thanked: 447 times

by Rahul@gurome » Sun Aug 08, 2010 7:07 pm

Jinglander wrote:Hey guys sorry I dont have an answer for this

A jury of 12 is to be selected from a pool of 15. 2/3 are male 1/3 are female. What is the probability that the selected jury will be 2/3 male

Here's another way to approach the question:

A jury of 12 members is to be selected, in which 2/3 of the members should be male.
Now 2/3 of 12 = 2*4 = 8. So, the male members can be 8, 9 or 10.
If there are 8 males, then females = 4
If there are 9 males, then females = 3
If there are 10 males, then females = 2

So, No. of favorable possibilities = 10C8 * 5C4 + 10C9 * 5C3 + 10C10 * 5C2 = 45*5 + 10*10 + 1*10 = 225 + 100 + 10 = 335
Total no. of possibilities = 15C12 = 455

So, required probability = 335/455 = 67/91

Does that help?

Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)

Like this post

Jinglander: Senior | Next Rank: 100 Posts; Posts: 58; Joined: Thu Jul 22, 2010 5:40 pm; Thanked: 1 times

by Jinglander » Sun Aug 08, 2010 7:31 pm

With the solution with that 1-p(7)

you can only use this because you know 7 men is the only negative outcome. if you were choosing from 16 jurors then you could also have 6 men

Like this post

sheelanadh: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Thu Aug 05, 2010 3:43 am

by sheelanadh » Mon Aug 09, 2010 10:12 am

Rahul@gurome wrote:
Jinglander wrote:Hey guys sorry I dont have an answer for this

A jury of 12 is to be selected from a pool of 15. 2/3 are male 1/3 are female. What is the probability that the selected jury will be 2/3 male
Here's another way to approach the question:

A jury of 12 members is to be selected, in which 2/3 of the members should be male.
Now 2/3 of 12 = 2*4 = 8. So, the male members can be 8, 9 or 10.
If there are 8 males, then females = 4
If there are 9 males, then females = 3
If there are 10 males, then females = 2

So, No. of favorable possibilities = 10C8 * 5C4 + 10C9 * 5C3 + 10C10 * 5C2 = 45*5 + 10*10 + 1*10 = 225 + 100 + 10 = 335
Total no. of possibilities = 15C12 = 455

So, required probability = 335/455 = 67/91

Does that help?

thank u..is there any way to solve this problem....

Like this post

Post new topic Post Reply

• Page 1 of 1

GMAT Course Reviews

559 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (560 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review