BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Manhattan GMAT

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 120
Joined: Mon Nov 07, 2011 10:54 pm
Location: Delhi
Thanked: 5 times
by bryan88 » Sun May 06, 2012 10:03 am
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?
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 385
Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members
Location: Pune, India
Thanked: 186 times

by aneesh.kg » Sun May 06, 2012 10:25 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
= [spoiler]67/91 (Option D)[/spoiler]

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)
= [spoiler]67/91 (Option D)[/spoiler]

Same Answer.
Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 120
Joined: Mon Nov 07, 2011 10:54 pm
Location: Delhi
Thanked: 5 times

by bryan88 » Sun May 06, 2012 10:40 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.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3835
Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members
Location: Milpitas, CA
Thanked: 1854 times
GMAT Score:770

by Anurag@Gurome » Sun May 06, 2012 7:55 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)
= [spoiler]67/91[/spoiler]

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

Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1