GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Jul 2018, 14:17

Close

GMAT Club Daily Prep

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.

Close

Request Expert Reply

Confirm Cancel

The membership of a committee consists of 3 English teachers

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
User avatar
Joined: 06 Apr 2010
Posts: 134
Reviews Badge
The membership of a committee consists of 3 English teachers  [#permalink]

Show Tags

New post Updated on: 29 Nov 2013, 14:15
11
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

82% (00:40) correct 18% (00:54) wrong based on 450 sessions

HideShow timer Statistics

The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be English teachers?

A. 2/3
B. 1/3
C. 2/9
D. 1/12
E. 1/24

Originally posted by udaymathapati on 02 Sep 2010, 13:15.
Last edited by Bunuel on 29 Nov 2013, 14:15, edited 1 time in total.
RENAMED THE TOPIC.
Most Helpful Expert Reply
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47112
Re: Teacher selection  [#permalink]

Show Tags

New post 02 Sep 2010, 13:53
udaymathapati wrote:
The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be English teachers?
A. 2/3
B. 1/3
C. 2/9
D. 1/12
E. 1/24


There are total 3+4+2=9 teachers out of which 3 teach English.

\(P=\frac{C^2_3}{C^2_9}=\frac{1}{12}\)

Or: \(P=\frac{3}{9}*\frac{2}{8}=\frac{1}{12}\).

Answer: D.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Most Helpful Community Reply
6 KUDOS received
Manager
Manager
User avatar
Joined: 06 Oct 2009
Posts: 58
Re: Teacher selection  [#permalink]

Show Tags

New post 14 Sep 2010, 07:02
6
Probability of first member an English teacher = 3/9
Probability of second member an English teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (D)
_________________

+1 kudos me if this is of any help...

General Discussion
Intern
Intern
avatar
Joined: 25 Aug 2010
Posts: 1
Re: Teacher selection  [#permalink]

Show Tags

New post 14 Sep 2010, 00:43
Hello Bunuel,

Can you please explain why you have used combinations instead of permutations to calculate the probability?

Thanks in advance,
Manager
Manager
avatar
Joined: 30 Aug 2010
Posts: 89
Location: Bangalore, India
Re: Teacher selection  [#permalink]

Show Tags

New post 14 Sep 2010, 04:54
Hi sarafbhushan,

The combinatioan has to be used due to the below reason.

Let us say if we have 3 people A, B and C. If we are asked to select a couple. we can select AB/BC/CA: Please mnote that selecting AB is same as selecting BA as my couple is same in both the cases. Same is the case with selection teachers for a committee, as is the case in the question.

3C2 = 3C1 (not selecting 1) = 3 (AB, BC, CA)
3P2 = 6 (If Ab is not = BA)

Hope it is clear
Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47112
Re: Teacher selection  [#permalink]

Show Tags

New post 14 Sep 2010, 06:16
sarafbhushan wrote:
Hello Bunuel,

Can you please explain why you have used combinations instead of permutations to calculate the probability?

Thanks in advance,


As explained above, order of the members in the committee is not important. For example, \(C^2_9\) gives the # of all committees of 2 we can choose out of 9 teachers (a, b, c, d, e, f, g, h, i): (a, b), (a,c), (a,d), ... Now, committee (a,b) is the same committee as (b,a), so that's why we should use C (which counts (a,b) only once) instead of P (which counts (a,b) as well (b,a)).

Check Probability and Combinations chapters of Math Book for more on this issues (link in my signature).

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 16 Oct 2010
Posts: 83
Location: United States
Concentration: Finance, Entrepreneurship
GMAT 1: 700 Q49 V35
WE: Information Technology (Investment Banking)
Re: Membership of committee  [#permalink]

Show Tags

New post 25 Oct 2010, 05:38
monirjewel wrote:
The membership of committee consists of 3 English teachers, 4 mathematics teacher, and 2 social studies teachers. If 2 committee members are to be selected at random to write the committee's report, what is the probability that the two members selected will be both be English teachers?
A) 2/3
B) 1/3
C) 2/9
D) 1/12
E 1/24


My approach would be-
3C2/9C2 = 1/12

I am not sure why the OA is (C).
Intern
Intern
avatar
B
Joined: 24 Oct 2016
Posts: 22
Re: The membership of a committee consists of 3 English teachers  [#permalink]

Show Tags

New post 28 Dec 2017, 19:56
Hi all,

I was trying to solve this problem in reverse way and getting wrong answer. Im solving as “1 - probability of selecting both from maths and social” that is 1-6c2/9c2 = 7/12. Anyone explain where I went wrong .
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47112
Re: The membership of a committee consists of 3 English teachers  [#permalink]

Show Tags

New post 28 Dec 2017, 20:30
1
gvrk_77 wrote:
The membership of a committee consists of 3 English teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be English teachers?

A. 2/3
B. 1/3
C. 2/9
D. 1/12
E. 1/24

Hi all,

I was trying to solve this problem in reverse way and getting wrong answer. Im solving as “1 - probability of selecting both from maths and social” that is 1-6c2/9c2 = 7/12. Anyone explain where I went wrong .


The opposite event of both being English teachers is {both are Mathematics and Social teachers} + {one is English teacher and one is Mathematics or Social teacher}.

\(P=1 - (\frac{C^2_6}{C^2_9}+\frac{C^1_3*C^1_6}{C^2_9})=1-(\frac{15}{36}+\frac{18}{36})=\frac{1}{12}\)

Or: \(P=1-(\frac{6}{9}*\frac{5}{8}+2*\frac{3}{9}*\frac{6}{8})=\frac{1}{12}\) (we multiply 3/9*6/8 by 2 because English/Not English can occur in two ways: {English, Not English} and {Not English, English}).

Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: The membership of a committee consists of 3 English teachers &nbs [#permalink] 28 Dec 2017, 20:30
Display posts from previous: Sort by

The membership of a committee consists of 3 English teachers

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Events & Promotions

PREV
NEXT


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.