Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Oct 2014, 20:36

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

In a drawer of shirts 8 are blue, 6 are green and 4 are

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
SVP
SVP
User avatar
Joined: 16 Oct 2003
Posts: 1816
Followers: 4

Kudos [?]: 37 [1] , given: 0

In a drawer of shirts 8 are blue, 6 are green and 4 are [#permalink] New post 11 Dec 2005, 19:07
1
This post received
KUDOS
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (02:36) correct 38% (01:16) wrong based on 128 sessions
In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability at least one of the shirts he draws will be blue?

(A) 25/153
(B) 28/153
(C) 5/17
(D) 4/9
(E) 12/17
[Reveal] Spoiler: OA

Last edited by Bunuel on 27 Oct 2013, 05:28, edited 2 times in total.
Edited the question, added the OA and moved to PS forum.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jul 2004
Posts: 5097
Location: Singapore
Followers: 19

Kudos [?]: 149 [0], given: 0

 [#permalink] New post 11 Dec 2005, 19:39
1
This post was
BOOKMARKED
Assume no replacement:
P(1 blue and 1 other colour) = 8/18 * 10/17 = 40/153
P(1 blue and 1 blue) = 8/18 * 7/17 = 28/153

40/153 + 28/153 = 4/9 is the probability at least one is blue
VP
VP
avatar
Joined: 06 Jun 2004
Posts: 1061
Location: CA
Followers: 2

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

 [#permalink] New post 11 Dec 2005, 19:50
Does it matter if he draws the shirts at once or in order.....
1 KUDOS received
Intern
Intern
avatar
Joined: 18 Jul 2003
Posts: 12
Followers: 0

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

 [#permalink] New post 12 Dec 2005, 00:45
1
This post received
KUDOS
I think its E

there are a total of 18 shirts. 8 blue and 10 non blue.

P(selecting at least 1 blue shirt) = 1 - P(selecting no blue shirts)

Assuming no replacement

P(selecting first non-blue shirt) = 10/18
P(selecting secong non-blue shirt) = 9/17

P(selecting no blue shirts) = 10/18 * 9/17= 10/34

Therefor P(selecting at least 1 blue shirt) = 1 -(10/34)= 24/34=12/17
Current Student
User avatar
Joined: 29 Jan 2005
Posts: 5252
Followers: 23

Kudos [?]: 135 [0], given: 0

Reviews Badge
 [#permalink] New post 12 Dec 2005, 07:07
Lucky Twin + intuition guess (must be more than 50%) 12/17.

(E)
1 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 14 Apr 2005
Posts: 422
Location: India, Chennai
Followers: 1

Kudos [?]: 3 [1] , given: 0

Re: Probability:Blue Shirt [#permalink] New post 14 Dec 2005, 00:16
1
This post received
KUDOS
Bhai wrote:
16. In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability at least one of the shirts he draws will be blue?

(A)25/153
(B)28/153
(C)5/17
(D)4/9
(E)12/17


= 1 - p(None of them being blue)
= 1 - (10/18 * 9 /17)
= 1 - 5/17
= 12/17 E
Intern
Intern
avatar
Joined: 26 Oct 2013
Posts: 1
Followers: 0

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

Re: In a drawer of shirts 8 are blue, 6 are green and 4 are [#permalink] New post 26 Oct 2013, 14:51
Its may be blue but i m not sure....
Intern
Intern
avatar
Joined: 19 Sep 2013
Posts: 21
GMAT 1: 720 Q49 V38
GPA: 3.8
Followers: 0

Kudos [?]: 14 [0], given: 17

Re: [#permalink] New post 26 Oct 2013, 20:58
ywilfred wrote:
Assume no replacement:
P(1 blue and 1 other colour) = 8/18 * 10/17 = 40/153
P(1 blue and 1 blue) = 8/18 * 7/17 = 28/153

40/153 + 28/153 = 4/9 is the probability at least one is blue


Hey, I think you went wrong here because there are 2 possibilities of him picking one blue and one other color.. Blue first then Random or Random first then Blue.. Which will double the probability .

80/153 + 28/153 = 12/17 :)
_________________

Kudos if you like my post :)

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23066
Followers: 3542

Kudos [?]: 27334 [0], given: 2734

Re: In a drawer of shirts 8 are blue, 6 are green and 4 are [#permalink] New post 27 Oct 2013, 05:32
Expert's post
1
This post was
BOOKMARKED
Bhai wrote:
In a drawer of shirts 8 are blue, 6 are green and 4 are magenta. If Mason draws 2 shirts at random, what is the probability at least one of the shirts he draws will be blue?

(A) 25/153
(B) 28/153
(C) 5/17
(D) 4/9
(E) 12/17


P(at least one blue) = 1- P(0 blue) = 1 - 10/18*9/17 = 12/17.

Answer: E.

Some "at least" probability questions to practice:
leila-is-playing-a-carnival-game-in-which-she-is-given-140018.html
a-fair-coin-is-tossed-4-times-what-is-the-probability-of-131592.html
for-each-player-s-turn-in-a-certain-board-game-a-card-is-132074.html
a-string-of-10-light-bulbs-is-wired-in-such-a-way-that-if-131205.html
a-shipment-of-8-tv-sets-contains-2-black-and-white-sets-and-53338.html
on-a-shelf-there-are-6-hardback-books-and-2-paperback-book-135122.html
in-a-group-with-800-people-136839.html
the-probability-of-a-man-hitting-a-bulls-eye-in-one-fire-is-136935.html
for-each-player-s-turn-in-a-certain-board-game-a-card-is-141790.html
the-probability-that-a-convenience-store-has-cans-of-iced-128689.html
triplets-adam-bruce-and-charlie-enter-a-triathlon-if-132688.html
a-manufacturer-is-using-glass-as-the-surface-144642.html
the-probability-is-1-2-that-a-certain-coin-will-turn-up-head-144730.html (OG13)
a-fair-coin-is-to-be-tossed-twice-and-an-integer-is-to-be-148779.html
in-a-game-one-player-throws-two-fair-six-sided-die-at-the-151956.html
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23066
Followers: 3542

Kudos [?]: 27334 [0], given: 2734

Re: [#permalink] New post 27 Oct 2013, 05:34
Expert's post
TeHCM wrote:
Does it matter if he draws the shirts at once or in order.....


Mathematically the probability of picking 2 shirts simultaneously, or picking them one at a time (without replacement) is the same.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 17 May 2012
Posts: 5
Followers: 0

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

Re: Re: [#permalink] New post 21 May 2014, 14:11
Hi Bunuel,
Please find my doubt below.

q:In a drawer of shirts, 8 are blue, 6 are green, and 4 are red. If Miles draws two shirts at random, what is the probability that at least one of the shirts he draws is blue?

My approach:1-(zero shirts blue)

1-(10*9)/18c2

1-(10/17)=7/17.

Wrong..


Another approach:1-(10/18*9/17)

1-(5/17)=12/17

Right..

My doubts:1.When picking two shirts at random from a group of 18,is it not 18c2 for a total number of possibilities

2.Also,does "picking at random" means "picking simultaneously?"

3.Does ordering in this case matter?When should the order be considered and when it shouldnt be?Could you please throw some light on this?



Please rectify

Thank you

Regards,
Kona
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23066
Followers: 3542

Kudos [?]: 27334 [1] , given: 2734

Re: Re: [#permalink] New post 22 May 2014, 03:19
1
This post received
KUDOS
Expert's post
kona wrote:
Hi Bunuel,
Please find my doubt below.

q:In a drawer of shirts, 8 are blue, 6 are green, and 4 are red. If Miles draws two shirts at random, what is the probability that at least one of the shirts he draws is blue?

My approach:1-(zero shirts blue)

1-(10*9)/18c2

1-(10/17)=7/17.

Wrong..



Another approach:1-(10/18*9/17)

1-(5/17)=12/17

Right..

My doubts:1.When picking two shirts at random from a group of 18,is it not 18c2 for a total number of possibilities

2.Also,does "picking at random" means "picking simultaneously?"

3.Does ordering in this case matter?When should the order be considered and when it shouldnt be?Could you please throw some light on this?



Please rectify

Thank you

Regards,
Kona


1. If you use combination approach then it should be P(at \ least \ one \ blue) = 1- P(0 \ blue) = 1 - \frac{C^2_{10}}{C^2_{18}} = \frac{12}{17}. So, your denominator was correct but the numerator was not. It should have been C^2_{10}: the number of ways to pick two not-blue shirts out of 10.

2. No. You can pick randomly one-by-one as well as simultaneously.

3.
Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html

Theory on probability problems: math-probability-87244.html

All DS probability problems to practice: search.php?search_id=tag&tag_id=33
All PS probability problems to practice: search.php?search_id=tag&tag_id=54

Tough probability questions: hardest-area-questions-probability-and-combinations-101361.html


Hope this helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Intern
Intern
avatar
Joined: 13 May 2014
Posts: 40
Concentration: General Management, Strategy
Followers: 0

Kudos [?]: 28 [0], given: 1

Re: Re: [#permalink] New post 22 May 2014, 04:30
kona wrote:
Hi Bunuel,
Please find my doubt below.

q:In a drawer of shirts, 8 are blue, 6 are green, and 4 are red. If Miles draws two shirts at random, what is the probability that at least one of the shirts he draws is blue?

My approach:1-(zero shirts blue)

1-(10*9)/18c2

1-(10/17)=7/17.

Wrong..


Another approach:1-(10/18*9/17)

1-(5/17)=12/17

Right..

My doubts:1.When picking two shirts at random from a group of 18,is it not 18c2 for a total number of possibilities

2.Also,does "picking at random" means "picking simultaneously?"

3.Does ordering in this case matter?When should the order be considered and when it shouldnt be?Could you please throw some light on this?



Please rectify

Thank you

Regards,
Kona


Hi Kona,
in your 1st approach , it should be :
1- (10C2)/(18C2) = 1 -5/17 = 12/17

Here 10C2 defines the no. of ways in which 2 shirts can be picked from 10 (6G +4R) t-shirts.
Your numerator calcn 10 *9 makes a difference b/w a particular pair of 1G1R and 1R1G, which are essentially the same.
So,for your calcn of numerator double counting is happening.

1.Denominator 18C2 is perfectly ok for picking two shirts at random/simultaneously
2.It means the same in the present question context
3.Order would not matter as it is the case of picking (and not arranging thereafter)

Please press Kudos if you wish to appreciate

*** Kudos is the best form of appreciation***
Intern
Intern
avatar
Joined: 19 May 2014
Posts: 31
Followers: 0

Kudos [?]: 3 [0], given: 6

Re: In a drawer of shirts 8 are blue, 6 are green and 4 are [#permalink] New post 22 May 2014, 13:30
Dear Kona

You asked: "When should the order be considered and when it shouldn't be?"

I'll try to help you with this doubt.

Let's say there are 26 small tiles lying in a heap. Each tile has one letter of the English alphabet inscribed on it, and no two tiles have the same alphabet. Now you are asked by the tile-owners to pick up 2 tiles from this heap.

They are simply asking you to pick up the tiles; they are not interested in the order in which you pick up the tiles. Nothing will happen to one tile because it was picked up first, or because it was picked up second. So, whether you pick up E first and J later, or J first and E later doesn't matter. So, you will simply apply the formula to select a bunch of r things out of a bunch of n things =nCr.

When would order matter?

It would matter if they had told you that they will start the name of their new-born baby with the alphabet on the first tile you picked up. And that if the alphabet on your second slide lies between A and G, you will get $10. So, in this case, there are consequences to the order in which the tiles were picked up. You may still have picked up E and J, but the order in which you picked up will decide whether the baby will be named Eugene or Jeannie, and whether you will get $10 or not.

So, let's now tackle a question: What is the probability that the baby's name started with E and you got $10?

Total number of ways to pick up 1st tile = 26
Total number of ways to pick up 2nd tile = 25
So, Total number of ways to pick up the two tiles = 26*25

(Note that we didn't take 26C2, because 26C2 applies when you are taking out a bunch of 2 things out of a bunch of 26 things and order doesn't matter)

Favorable Cases:
Total number of ways in which the 1st tile can be E = 1
Total number of ways in which $10 can be won on the second tile = 6 (There are 7 alphabets from A to G, but E has already been taken out in the first pick)

So, Desired probability = (1*6)/(26*25)
=3/325
_________________

Please press Kudos if you were helped by my post!

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4815
Location: Pune, India
Followers: 1134

Kudos [?]: 5190 [0], given: 164

Re: Re: [#permalink] New post 22 May 2014, 20:27
Expert's post
kona wrote:

3.Does ordering in this case matter?When should the order be considered and when it shouldnt be?Could you please throw some light on this?



Check out this post for a discussion on when order matters and when it doesn't:

http://www.veritasprep.com/blog/2013/08 ... er-matter/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

Veritas Prep Reviews

Re: Re:   [#permalink] 22 May 2014, 20:27
    Similar topics Author Replies Last post
Similar
Topics:
There are 50 balls. 20 are red, 20 are green, 6 are blue, 4 bkk145 6 30 Aug 2007, 17:24
There are 3 green; 4 yellow; and 5 blue balls in a sack. 6 ggarr 3 06 Feb 2007, 22:35
A drawer holds 4 red hats and 4 blue hats. What is the chillpill 14 12 Apr 2006, 19:18
A drawer holds 4 red hats and 4 blue hats. What is the jeeboombaa 3 05 Jan 2006, 07:57
In a drawer of shirts, 8 are blue, 6 are green, and 4 are gayathri 7 17 Jan 2005, 11:12
Display posts from previous: Sort by

In a drawer of shirts 8 are blue, 6 are green and 4 are

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.