It is currently 24 Nov 2017, 00:50

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

M15-18

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42355

Kudos [?]: 133182 [0], given: 12439

M15-18 [#permalink]

Show Tags

New post 16 Sep 2014, 00:55
Expert's post
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (01:24) correct 25% (02:11) wrong based on 88 sessions

HideShow timer Statistics

A basket contains 3 blue marbles, 3 red marbles, and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?

A. \(\frac{2}{21}\)
B. \(\frac{3}{25}\)
C. \(\frac{1}{6}\)
D. \(\frac{9}{28}\)
E. \(\frac{11}{24}\)
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 133182 [0], given: 12439

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42355

Kudos [?]: 133182 [0], given: 12439

Re M15-18 [#permalink]

Show Tags

New post 16 Sep 2014, 00:55
Official Solution:

A basket contains 3 blue marbles, 3 red marbles, and 3 yellow marbles. If 3 marbles are extracted from the basket at random, what is the probability that a marble of each color is among the extracted?

A. \(\frac{2}{21}\)
B. \(\frac{3}{25}\)
C. \(\frac{1}{6}\)
D. \(\frac{9}{28}\)
E. \(\frac{11}{24}\)

\(P=\frac{C^1_3*C^1_3*C^1_3}{C^3_9}=\frac{9}{28}\). Numerator represents ways to select 1 blue marble out of 3, 1 red marble out of 3 and 1 yellow marble out of 3. Denominator represents total ways to select 3 marbles out of 9.

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

Kudos [?]: 133182 [0], given: 12439

Intern
Intern
avatar
Joined: 21 May 2013
Posts: 7

Kudos [?]: 8 [0], given: 5

Re: M15-18 [#permalink]

Show Tags

New post 28 Dec 2014, 12:27
Could you explain please why this method does not work :

Probability of extracting 1 blue marble : 3/9
Probability of extracting the next one as red : 3/8
And the next one as yellow : 3/7

Which equals 3/9 * 3/8 * 3/7 = 9/56

Kudos [?]: 8 [0], given: 5

2 KUDOS received
Verbal Forum Moderator
avatar
Joined: 15 Apr 2013
Posts: 196

Kudos [?]: 881 [2], given: 30

Location: India
Concentration: General Management, Marketing
GMAT Date: 11-23-2015
GPA: 3.6
WE: Science (Other)
GMAT ToolKit User Premium Member Reviews Badge
Re: M15-18 [#permalink]

Show Tags

New post 23 Oct 2015, 23:16
2
This post received
KUDOS
Hello,

Old thread but might be useful to someone else.

filipTGIM your approach is partial.

You are assuming a defined sequence only i.e. Blue first, red second and yellow last. But don't you think there could be other possibilities also i.e. Red-Blue-Yellow...so on...

Basically three item can be arranged in 3*2*1= 6 ways and hence in the final step you need to multiply with 06.

Probability of extracting 1 blue marble : 3/9
Probability of extracting the next one as red : 3/8
And the next one as yellow : 3/7

Which equals 3/9 * 3/8 * 3/7 = 3/56 (not 9/56)

Then we need to multiply with 06:

3/56*6 = 18/56 or 09/28

Hope it helps!


Please hit kudos if you like this explanation

Kudos [?]: 881 [2], given: 30

Intern
Intern
avatar
Joined: 13 Jun 2016
Posts: 19

Kudos [?]: 1 [0], given: 2

Premium Member
Re: M15-18 [#permalink]

Show Tags

New post 20 Jun 2016, 07:37
combinatorics is my weakness but correct my if im wrong, the numerator of the answer should be addition not multiplication that equals 9?

you have 1C3∗1C3∗1C3 / 3C9 = 9/28

Kudos [?]: 1 [0], given: 2

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42355

Kudos [?]: 133182 [0], given: 12439

Re: M15-18 [#permalink]

Show Tags

New post 20 Jun 2016, 07:46
Expert's post
1
This post was
BOOKMARKED
lydennis8 wrote:
combinatorics is my weakness but correct my if im wrong, the numerator of the answer should be addition not multiplication that equals 9?

you have 1C3∗1C3∗1C3 / 3C9 = 9/28


No, it's multiplication, because of Principle of Multiplication. The result is 27/84, which when reduced gives 9/28.

Principle of Multiplication
If an operation can be performed in ‘m’ ways and when it has been performed in any of these ways, a second operation that can be performed in ‘n’ ways then these two operations can be performed one after the other in ‘m*n’ ways.

Principle of Addition
If an operation can be performed in ‘m’ different ways and another operation in ‘n’ different ways then either of these two operations can be performed in ‘m+n’ ways (provided only one has to be done).

Check below post for more:
Probability Made Easy!

Theory on probability problems

Data Sufficiency Questions on Probability
Problem Solving Questions on Probability

Tough Probability Questions
_________________

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

Kudos [?]: 133182 [0], given: 12439

Expert Post
Math Expert
User avatar
P
Joined: 02 Aug 2009
Posts: 5234

Kudos [?]: 5892 [0], given: 118

Re: M15-18 [#permalink]

Show Tags

New post 20 Jun 2016, 07:49
lydennis8 wrote:
combinatorics is my weakness but correct my if im wrong, the numerator of the answer should be addition not multiplication that equals 9?

you have 1C3∗1C3∗1C3 / 3C9 = 9/28


Hi
it will be multiplication...
\(3C1 = \frac{3!}{(3-1)!} = \frac{3!}{2!}= \frac{3*2*1}{2*1} = 3\)....
so numerator will become = 3*3*3..
denominator = \(9C3 = \frac{9!}{(9-3)!3!}= \frac{9*8*7*6!}{6!*3*2*1} = \frac{9*8*7}{3*2} = 3*4*7\)...
so fraction \(\frac{3C1*3C1*3C1}{9C3} = \frac{3*3*3}{3*4*7}= \frac{9}{28}\)
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5892 [0], given: 118

Intern
Intern
avatar
Joined: 02 Sep 2016
Posts: 10

Kudos [?]: 1 [0], given: 0

Re: M15-18 [#permalink]

Show Tags

New post 27 Sep 2016, 14:20
how to know if we need to multiply or add in the numerater?

Kudos [?]: 1 [0], given: 0

Intern
Intern
avatar
S
Joined: 13 Dec 2016
Posts: 45

Kudos [?]: 8 [0], given: 571

Re: M15-18 [#permalink]

Show Tags

New post 22 Jan 2017, 01:17
manchitkapoor wrote:
how to know if we need to multiply or add in the numerater?


I follow the below logic to decide when to multiply or add when solving Permutation / Combination problems :

If the problem states that we need to find the probability of Say A event AND B event - Use Multiplication

If the problem states that we need to find the probability of Say A event OR B event - Use Addition

Hope this helps.

Kudos [?]: 8 [0], given: 571

Intern
Intern
avatar
B
Joined: 05 Sep 2017
Posts: 4

Kudos [?]: 0 [0], given: 26

Re: M15-18 [#permalink]

Show Tags

New post 18 Sep 2017, 02:32
why do we use combinations and not permutations here? order does matter, I think

Kudos [?]: 0 [0], given: 26

Re: M15-18   [#permalink] 18 Sep 2017, 02:32
Display posts from previous: Sort by

M15-18

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

Moderators: chetan2u, Bunuel



GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.