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

It is currently 15 Dec 2018, 08:09

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 in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • $450 Tuition Credit & Official CAT Packs FREE

     December 15, 2018

     December 15, 2018

     10:00 PM PST

     11:00 PM PST

    Get the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)
  • FREE Quant Workshop by e-GMAT!

     December 16, 2018

     December 16, 2018

     07:00 AM PST

     09:00 AM PST

    Get personalized insights on how to achieve your Target Quant Score.

A bag contains 3 red, 4 black and 2 white balls. What is the probabili

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

Hide Tags

Intern
Intern
avatar
Joined: 24 Jul 2004
Posts: 14
A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post Updated on: 07 Apr 2018, 11:39
3
34
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

50% (00:58) correct 50% (00:50) wrong based on 975 sessions

HideShow timer Statistics

A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9

Originally posted by Keen on 26 Jul 2004, 09:33.
Last edited by Bunuel on 07 Apr 2018, 11:39, edited 3 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51218
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 23 Sep 2013, 06:53
4
3
A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9

This is with replacement case.

\(P=2*\frac{3}{9}*\frac{2}{9}=\frac{4}{27}\)

We are multiplying by 2 as there are two possible wining scenarios RW and WR.

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

General Discussion
Senior Manager
Senior Manager
avatar
Joined: 19 May 2004
Posts: 291
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 26 Jul 2004, 09:41
3
A is correct if you want to get a Red ball First and then a White one.
If the order doesn't matter, then the answer is D.

(2/27)*2 = 4/27
Intern
Intern
avatar
Joined: 24 Jul 2004
Posts: 14
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 26 Jul 2004, 10:14
1
This is how I came up with 2/27. the probability of getting one red is 3/9 (nine is the total number of balls). The probability of getting a white ball is 2/9 (9 again because the ball is put back after each draw) so 3/9*2/9 + 6/81 = 2/27

according to Dookie (who is right) if they are asking for the balls to draw one of the the other, which they are (successive draws) you have to multiply 2/27 by 2 = 4/27.
Joined: 31 Dec 1969
Location: Russian Federation
Concentration: Entrepreneurship, International Business
WE: Supply Chain Management (Energy and Utilities)
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 31 Jul 2004, 06:53
1
1
Here is how I solved it

First of all we have
Probability of drawing a Red ball is 3/9
Probability of drawing a White ball is 3/9

There are two ways in which the balls can be drawn


Case 1: Red ball in the first draw and white in the second draw
Hence the combined Probability is 3/9*2/9=6/81

Case 2: White ball in the first draw and red in the second draw
Hence the combined Probability is 2/9*3/9=6/81

both these cases satisfy our requirement
Hence either of them will do i.e OR
Hence the final probability comes to be
Case 1 OR Case 2 = 6/81 + 6/81 (OR means addition)
Hence the Ans is 12/81=4/27
Senior Manager
Senior Manager
avatar
Joined: 07 Sep 2010
Posts: 261
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 23 Sep 2013, 19:22
1
Hello Bunuel,
I m a bit confused about when to consider and when not to consider. I am having a tough time understanding this concept. I was under the impression that in "with replacement" cases, we dont need to consider the cases, however in without replacement cases, scenarios needs to be considered.

In addition,I found this link, where the question is also testing the same concept, but we didn't consider the multiple cases here. Please clarify.
http://gmatclub.com/forum/rich-has-3-gr ... 55253.html


Can you provide a high level conceptual knowledge as in when to consider cases and when not to?
Pls help.

Posted from my mobile device
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 27 Sep 2013, 19:21
4
imhimanshu wrote:
Hello Bunuel,
I m a bit confused about when to consider and when not to consider. I am having a tough time understanding this concept. I was under the impression that in "with replacement" cases, we dont need to consider the cases, however in without replacement cases, scenarios needs to be considered.

In addition,I found this link, where the question is also testing the same concept, but we didn't consider the multiple cases here. Please clarify.
http://gmatclub.com/forum/rich-has-3-gr ... 55253.html


Can you provide a high level conceptual knowledge as in when to consider cases and when not to?
Pls help.

Posted from my mobile device


Responding to a pm:

The status of "replacement" has nothing to do with the "sequence". It only changes the probability.

Say we have 2 red and 3 white balls in a bag. We pull out two one after another with replacement. What is the probability that one is red and the other is white.
Now note that there are 4 ways in which you can pull out two balls from the bag:
1. You pull a Red and then a Red again RR - (2/5)*(2/5) (Note that it is with replacement)
2. You pull a Red and then a White RW - (2/5)*(3/5)
3. You pull a White and then a Red WR - (3/5)*(2/5)
4. You pull a White and then a White WW - (3/5)*(3/5)

Total probability = (2/5)*(2/5) + (2/5)*(3/5) + (3/5)*(2/5) + (3/5)*(3/5) = 1

In how many cases do we have a red and a white ball? In case 2 and case 3.
Probability of picking a red and a white with replacement = (2/5)*(3/5) + (3/5)*(2/5) = (3/5)*(2/5) * 2
Since the probability of picking a red and then a white is same as probability of picking a white and then a red, you simply write down one case and multiply it by 2. You do the same in case of 'without replacement' too. The only thing that changes is the probability.

Without Replacement:
1. You pull a Red and then a Red again RR - (2/5)*(1/4)
2. You pull a Red and then a White RW - (2/5)*(3/4)
3. You pull a White and then a Red WR - (3/5)*(2/4)
4. You pull a White and then a White WW - (3/5)*(2/4)
Probability of picking a red and a white WITHOUT replacement = (2/5)*(3/4) + (3/5)*(2/4) = (3/5)*(2/4) * 2

As for the link you have mentioned, this is exactly what is done there too. Check it out - I will show you how it is done there.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Manager
Manager
User avatar
Joined: 20 Jan 2014
Posts: 144
Location: India
Concentration: Technology, Marketing
GMAT ToolKit User
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 22 Sep 2014, 05:33
VeritasPrepKarishma wrote:
imhimanshu wrote:
Hello Bunuel,
I m a bit confused about when to consider and when not to consider. I am having a tough time understanding this concept. I was under the impression that in "with replacement" cases, we dont need to consider the cases, however in without replacement cases, scenarios needs to be considered.

In addition,I found this link, where the question is also testing the same concept, but we didn't consider the multiple cases here. Please clarify.
http://gmatclub.com/forum/rich-has-3-gr ... 55253.html


Can you provide a high level conceptual knowledge as in when to consider cases and when not to?
Pls help.

Posted from my mobile device


Responding to a pm:

The status of "replacement" has nothing to do with the "sequence". It only changes the probability.

Say we have 2 red and 3 white balls in a bag. We pull out two one after another with replacement. What is the probability that one is red and the other is white.
Now note that there are 4 ways in which you can pull out two balls from the bag:
1. You pull a Red and then a Red again RR - (2/5)*(2/5) (Note that it is with replacement)
2. You pull a Red and then a White RW - (2/5)*(3/5)
3. You pull a White and then a Red WR - (3/5)*(2/5)
4. You pull a White and then a White WW - (3/5)*(3/5)

Total probability = (2/5)*(2/5) + (2/5)*(3/5) + (3/5)*(2/5) + (3/5)*(3/5) = 1

In how many cases do we have a red and a white ball? In case 2 and case 3.
Probability of picking a red and a white with replacement = (2/5)*(3/5) + (3/5)*(2/5) = (3/5)*(2/5) * 2
Since the probability of picking a red and then a white is same as probability of picking a white and then a red, you simply write down one case and multiply it by 2. You do the same in case of 'without replacement' too. The only thing that changes is the probability.

Without Replacement:
1. You pull a Red and then a Red again RR - (2/5)*(1/4)
2. You pull a Red and then a White RW - (2/5)*(3/4)
3. You pull a White and then a Red WR - (3/5)*(2/4)
4. You pull a White and then a White WW - (3/5)*(2/4)
Probability of picking a red and a white WITHOUT replacement = (2/5)*(3/4) + (3/5)*(2/4) = (3/5)*(2/4) * 2

As for the link you have mentioned, this is exactly what is done there too. Check it out - I will show you how it is done there.



Thank You Karishma.
I got a key concept here :)

But i am more comfortable by Combination method

1C3*1C2/ (1C9 * 1C9)
= 6/81 = 2/27

Now we can get this in two ways (as described by u)
2* 2/27 = 4/27
_________________

Consider +1 Kudos Please :)

SVP
SVP
avatar
B
Joined: 06 Nov 2014
Posts: 1880
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 16 Jul 2016, 11:45
Keen wrote:
A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9

Please explain your answer. I came up with but that is wrong.


3R, 4B, 2W balls.

P(1R, 1W) = (3/9)*(2/9) = 1/3*2/9 = 2/27
Now the Red and the While balls can be drawn in any order
Hence probability = 2*2/27 = 4/27

Correct Option: D
Intern
Intern
avatar
B
Joined: 14 Aug 2017
Posts: 42
Concentration: Operations, Social Entrepreneurship
GMAT 1: 610 Q48 V26
GMAT ToolKit User
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 25 Oct 2017, 00:52
karishma Bunuel - Can you please explain as to where my concept is headed in the wrong direction?

At first i saw that there are 9 balls and 2 balls are to be drawn, i selected the 2 balls out of 9 (9C2) giving me the total outcomes and next when i am supposed to draw the balls in the manner of white and red it clicked to me that there are 4 case,
1 - RR
2 - RW
3 - WR
4 - WW

and i applied the same logic to the above 4 cases, but the answer did not match?

Can you please help me with this.

Thanks in advance.
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 26 Oct 2017, 21:58
1
siddyj94 wrote:
karishma Bunuel - Can you please explain as to where my concept is headed in the wrong direction?

At first i saw that there are 9 balls and 2 balls are to be drawn, i selected the 2 balls out of 9 (9C2) giving me the total outcomes and next when i am supposed to draw the balls in the manner of white and red it clicked to me that there are 4 case,
1 - RR
2 - RW
3 - WR
4 - WW

and i applied the same logic to the above 4 cases, but the answer did not match?

Can you please help me with this.

Thanks in advance.


Note that you cannot use 9C2 here because you are drawing balls with replacement.
9C2 means draw 2 balls out of 9 or draw 1 out of 9 and then 1 out of 8.
But here, we need to draw 1 out of 9 and then again 1 out of 9 (since the first ball is put back)

Also, why only 4? Wouldn't we have other cases too such as a Red and a Black?

Look at the solutions above to see how to solve it.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 29 Oct 2017, 06:41
1
Keen wrote:
A bag contains 3 red, 4 black and 2 white balls. What is the probability of drawing a red and a white ball in two successive draws, each ball being put back after it is drawn?

(A) 2/27
(B) 1/9
(C) 1/3
(D) 4/27
(E) 2/9


There are 9 balls in the bag, so the probability of drawing a red ball is P(Red) = 3/9 = ⅓, and the probability of drawing a white ball is P(White) = 2/9. We will draw two balls, replacing each ball after it is drawn.

The probability of drawing a red ball first and then a white ball is: P(Red) x P(White) = ⅓ x 2/9 = 2/27. But we can also draw a white ball first and then a red ball: P(White) x P(Red) = 2/9 x ⅓ = 2/27. Either of these outcomes satisfies our outcome of interest, and so we add the two probabilities: 2/27 + 2/27 = 4/27.

Answer: D
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13087
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 25 Nov 2017, 14:15
1
Hi All,

We're told that a bag contains 3 red, 4 black and 2 white balls. We're asked for the probability of drawing a red and a white ball in two successive draws, while replacing each ball after it is drawn.

The prompt does NOT state that the red ball has to be drawn first, so there are two options that we have to consider: red first, white second and white first, red second.

The probability of pulling a red first and a white second (with replacement) = (3/9)(2/9) = 6/81
The probability of pulling a while first and a red second (with replacement) = (2/9)(3/9) = 6/81
The total probability of pulling a red and white ball is 6/81 + 6/81 = 12/81 = 4/27

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 9164
Premium Member
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

New post 26 Nov 2018, 07:27
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

GMAT Club Bot
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili &nbs [#permalink] 26 Nov 2018, 07:27
Display posts from previous: Sort by

A bag contains 3 red, 4 black and 2 white balls. What is the probabili

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


Copyright

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®.