It is currently 23 Feb 2018, 04:37

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

A bag contains 5 white marbles and 5 black marbles. If each of 5 girls

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

Hide Tags

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43893
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 20 Jan 2015, 05:40
1
This post received
KUDOS
Expert's post
7
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

68% (01:37) correct 32% (01:43) wrong based on 163 sessions

HideShow timer Statistics

A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.
[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

4 KUDOS received
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 721
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 20 Jan 2015, 21:28
4
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.


Consider a case when all girls select black marbles...So Girl 1 will chose 1 black marble out of 10..and black marble will be chosen from 5 Black marbles

Girl 1 will have a probability of picking black marble 5/10
Girl 2 will have to pick a black marble out of 4 and total remaining no. of marbles 9=4/9

So we have Probability of all girls selecting black marbles as 5/10*4/9*3/8*2/7*1/6 =1/252

Since Girls can also select white marbles so we will have 2 cases so Probability of girls selecting all same colour marbles is 2*1/252 or 1/126

Ans is A
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

3 KUDOS received
Manager
Manager
User avatar
Joined: 03 Sep 2014
Posts: 75
Concentration: Marketing, Healthcare
Premium Member
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 07 May 2015, 07:23
3
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.


First girl can pick any marble, rest of the girls should pick same as her

=> P(First Girl) = \(\frac{10}{10}\)(as she can choose any marble) and rest follows;

=> \(1*\frac{4}{9}*\frac{3}{8}*\frac{2}{7}*\frac{1}{6} = \frac{1}{126}\)

Hence Answer is A
Current Student
User avatar
Status: I am ready!
Joined: 05 Nov 2014
Posts: 52
Location: India
GMAT 1: 700 Q49 V35
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 24 May 2015, 02:35
total possibilities: 5 girls can choose any 5 of the 10 marbles => 10c5
Total favourable: all 5 girls choose only white or black = 2 posibilities

Answer= (2/10c5) ::A
Manager
Manager
User avatar
Joined: 16 Jan 2015
Posts: 52
Location: United States
Schools: Kellogg '17, ISB '17
GMAT Date: 05-20-2015
GPA: 3.06
WE: Business Development (Commercial Banking)
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 24 May 2015, 02:45
10/10 * 4/9 * 3/8 * 2/7 * 1/6 = 1/126

Option A is the answer
1 KUDOS received
Intern
Intern
avatar
Joined: 16 May 2015
Posts: 14
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 26 May 2015, 05:15
1
This post received
KUDOS
Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.


Please let me know if my logic is correct

I looked at as.
first, total ways to select for all boys and girls,
that is, 10!/(5!*5!)= 252
then there are one two way girls can have all same colors, either white or black.

Therefore, total favorable outcomes/total outcomes = 2/252= 1/126
Expert Post
2 KUDOS received
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 806
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 27 May 2015, 00:59
2
This post received
KUDOS
Expert's post
shallow9323 wrote:
Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.


Please let me know if my logic is correct

I looked at as.
first, total ways to select for all boys and girls,
that is, 10!/(5!*5!)= 252
then there are one two way girls can have all same colors, either white or black.

Therefore, total favorable outcomes/total outcomes = 2/252= 1/126


Dear shallow9323

Your logic is perfectly correct! :)

For the benefit of other students reading this thread, this alternate approach is described in detail below:

Total number of ways in which the 5 girls can select 5 balls out of 10 balls = 10C5 = 10!/(5!*5!) = 252
(Note: Once the girls select 5 balls, the remaining 5 balls are automatically selected for boys)

The number of ways in which 5 girls can select 5 white balls = 5C5 = 1 (because there are only 5 white balls and all of them have to be selected)
The number of ways in which 5 girls can select 5 black balls = 5C5 = 1

So, number of favorable cases = (No. of ways to select 5 White balls) + (No. of ways to select 5 black balls) = 1 + 1 = 2

So, probability of Event = 2/252 = 1/126
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Senior Manager
Senior Manager
User avatar
G
Joined: 03 Apr 2013
Posts: 290
Location: India
Concentration: Marketing, Finance
Schools: Simon '20
GMAT 1: 740 Q50 V41
GPA: 3
GMAT ToolKit User
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 24 Nov 2016, 20:34
Bunuel wrote:
A bag contains 5 white marbles and 5 black marbles. If each of 5 girls and 5 boys randomly selects and keeps a marble, what is the probability that all of the girls select the same colored marble?

A. 1/126
B. 1/120
C. 1/24
D. 4/25
E. 1/2

Kudos for a correct solution.


Bunuel
Please help.. to count the number of all possible outcomes..we have used
\(10c5\)
But this is used when all of the objects are distinct..but here there are 5 similar things of one kind and 5 of the other. Please elaborate on this..as this will help me understand a lot.
_________________

Spread some love..Like = +1 Kudos :)

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13790
Premium Member
Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls [#permalink]

Show Tags

New post 11 Feb 2018, 20:23
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: A bag contains 5 white marbles and 5 black marbles. If each of 5 girls   [#permalink] 11 Feb 2018, 20:23
Display posts from previous: Sort by

A bag contains 5 white marbles and 5 black marbles. If each of 5 girls

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


cron

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®.