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

 It is currently 21 May 2019, 21:56

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

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

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

Author Message
TAGS:

Hide Tags

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

Show Tags

Updated on: 07 Apr 2018, 12:39
3
36
00:00

Difficulty:

75% (hard)

Question Stats:

51% (01:25) correct 49% (01:18) wrong based on 1058 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, 10:33.
Last edited by Bunuel on 07 Apr 2018, 12:39, edited 3 times in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
Math Expert
Joined: 02 Sep 2009
Posts: 55231
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

23 Sep 2013, 07:53
4
4
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.

_________________
General Discussion
Senior Manager
Joined: 19 May 2004
Posts: 287
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

26 Jul 2004, 10:41
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
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

26 Jul 2004, 11:14
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
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

31 Jul 2004, 07:53
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
Joined: 07 Sep 2010
Posts: 256
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

23 Sep 2013, 20:22
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
Joined: 16 Oct 2010
Posts: 9230
Location: Pune, India
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

27 Sep 2013, 20:21
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

Manager
Joined: 20 Jan 2014
Posts: 140
Location: India
Concentration: Technology, Marketing
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

22 Sep 2014, 06:33
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
_________________
SVP
Joined: 06 Nov 2014
Posts: 1877
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

16 Jul 2016, 12:45
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

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
Joined: 14 Aug 2017
Posts: 43
Concentration: Operations, Social Entrepreneurship
GMAT 1: 610 Q48 V26
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

25 Oct 2017, 01:52
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?

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9230
Location: Pune, India
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

26 Oct 2017, 22:58
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?

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

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

29 Oct 2017, 07:41
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.

_________________

Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14188
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

25 Nov 2017, 15:15
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

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

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

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/
Non-Human User
Joined: 09 Sep 2013
Posts: 10980
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili  [#permalink]

Show Tags

26 Nov 2018, 08:27
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.
_________________
Re: A bag contains 3 red, 4 black and 2 white balls. What is the probabili   [#permalink] 26 Nov 2018, 08:27
Display posts from previous: Sort by