Welcome! Check out our free B-School Guides to learn how you compare with other applicants.

## Manhattan GMAT

This topic has 1 expert reply and 2 member replies
bryan88 Really wants to Beat The GMAT!
Joined
07 Nov 2011
Posted:
120 messages
Thanked:
4 times
Manhattan GMAT Sun May 06, 2012 11:03 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
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?

A) 24/91
B) 45/91
C) 2/3
D) 67/91
E) 84/91

What is the 1-x method to this?

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
aneesh.kg GMAT Destroyer!
Joined
16 Apr 2012
Posted:
382 messages
Followed by:
24 members
Thanked:
174 times
Sun May 06, 2012 11:25 am
A team of 12 has to be selected from a pool of 10 men and 5 women.

The 1-x method:
The only unfavourable case is when in the team of 12, we have 7 Men and 5 Women.
So, we will subtract the probability of that from 1.

The required probability is:
1 - [P(7M,5W)]
= 1 - [10C7*5C5/15C12]
= 1 - (120/455)
= 335/455
= 67/91 (Option D)

Alternatively:
We will add up the probability of all the favourable outcomes.

The required probability is:
P(8M,4W) + P(9M,3W) + P(10M, 2W)
= 10C8*5C4 / 15C12 + 10C9*5C3 / 15C12 + 10C10*5C2 / 15C12
= (45*5 + 10*10 + 1*10)/(5*7*13)
= 67/91 (Option D)

_________________
Aneesh Bangia
GMAT Math Coach
aneesh.bangia@gmail.com

Thanked by: dipzzz
bryan88 Really wants to Beat The GMAT!
Joined
07 Nov 2011
Posted:
120 messages
Thanked:
4 times
Sun May 06, 2012 11:40 am
A case of 6 men and 6 women wont exists as the number of women is capped at 5.
Tricky question under time constraints.

### GMAT/MBA Expert

Anurag@Gurome GMAT Instructor
Joined
02 Apr 2010
Posted:
3835 messages
Followed by:
465 members
Thanked:
1754 times
GMAT Score:
770
Sun May 06, 2012 8:55 pm
bryan88 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?

A) 24/91
B) 45/91
C) 2/3
D) 67/91
E) 84/91

What is the 1-x method to this?
The following combinations are possible: (8M, 4W), (9M, 3W), (10M, 2W)
Total number of ways of selecting a jury of 12 people from 15 people = 15C12 = (15 * 14 * 13)/3 * 2) = 5 * 7 * 13
Required Probability = (10C8 * 5C4) + (10C9 * 5C3) + (10C10 * 5C2)/(5 * 7 * 13)
= [(5 * 9 * 5) + (10 * 5 * 2) + (5 * 2)]/(5 * 7 * 13)
= [(9 * 5) + (10 * 2) + 2]/(7 * 13)
= 67/91

_________________
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

GMAT with Gurome

### Best Conversation Starters

1 vipulgoyal 32 topics
2 hemant_rajput 23 topics
3 guerrero 18 topics
4 abhirup1711 17 topics
5 sana.noor 16 topics
See More Top Beat The GMAT Members...

### Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

211 posts
2 GMATGuruNY

The Princeton Review Teacher

137 posts
3 Jim@StratusPrep

Stratus Prep

60 posts