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

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A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink]

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26 Jul 2004, 09:33
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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

[Reveal] Spoiler:
A
but that is wrong.
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Sep 2013, 06:52, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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26 Jul 2004, 09:41
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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
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26 Jul 2004, 09:46
agree with Dookie....here the events are independent....
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26 Jul 2004, 10:02
Karthik wrote:
agree with Dookie....here the events are independent....

can you post a detail explanation ? thanks
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26 Jul 2004, 10:14
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rahul wrote:
Karthik wrote:
agree with Dookie....here the events are independent....

can you post a detail explanation ? thanks

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.
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31 Jul 2004, 06:53
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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
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31 Jul 2004, 06:59
Sorry for the Typo above
the Probability of drawing the white ball is 2/9

I posted the above explanation but just forgot to login
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05 Aug 2004, 18:51
Dookie wrote:
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

Dookie-

First red, then white:
drawing red: 3/9
drawing white: 2/9

3/9 * 2/9 = 2/27.

First white, the red:
2/9 * 3/9 = 2/27

how come order being matter would change the result?

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05 Aug 2004, 18:58
D is the right answer, without any mention about the other, we need to assume that the order is independent so it is

3/9 * 2/9 * 2 ( last 2 is for the order ) = 4/27
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Re: A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink]

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23 Sep 2013, 06:36
Bumping this thread as I am looking for experts to provide an explanation and confirm the OA.

Thanks
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Re: A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink]

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23 Sep 2013, 06:53
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imhimanshu wrote:
Bumping this thread as I am looking for experts to provide an explanation and confirm the OA.

Thanks

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.

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Re: A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink]

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23 Sep 2013, 19:22
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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.
rich-has-3-green-2-red-and-3-blue-balls-in-a-bag-he-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
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Re: A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink]

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27 Sep 2013, 19:21
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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.
rich-has-3-green-2-red-and-3-blue-balls-in-a-bag-he-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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Current Student Joined: 20 Jan 2014 Posts: 186 Location: India Concentration: Technology, Marketing Followers: 1 Kudos [?]: 58 [0], given: 120 A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink] ### Show Tags 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. rich-has-3-green-2-red-and-3-blue-balls-in-a-bag-he-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 GMAT Club Legend Joined: 09 Sep 2013 Posts: 13522 Followers: 577 Kudos [?]: 163 [0], given: 0 Re: A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink] ### Show Tags 01 Mar 2016, 08:34 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. _________________ Intern Joined: 28 Dec 2015 Posts: 42 Followers: 2 Kudos [?]: 2 [0], given: 62 Re: A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink] ### Show Tags 20 Jun 2016, 00:10 P(RW)---Remember that successive draws means one after another and it is not necessary that red will come before white,it can be vice versa too. So,First draw Red=3/9 Second draw White=2/9, Total number of balls will not change since we are putting back the balls in the bag. P(R and W)=3/9*2/9*2!=4/27 2!=RW or WR,any way you can draw the ball Senior Manager Joined: 02 Mar 2012 Posts: 374 Schools: Schulich '16 Followers: 4 Kudos [?]: 63 [0], given: 4 Re: A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink] ### Show Tags 20 Jun 2016, 05:31 answer will be D. If the question included the word'RESPECTIVELY' order would matter ..Then answer would be A if nothing is given order does not matter hope it helps Optimus Prep Instructor Joined: 06 Nov 2014 Posts: 1782 Followers: 51 Kudos [?]: 393 [0], given: 21 Re: A bag contains 3 red, 4 black and 2 white balls. What is the [#permalink] ### Show Tags 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 [Reveal] Spoiler: A 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 _________________ # Janielle Williams Customer Support Special Offer:$80-100/hr. Online Private Tutoring
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Re: A bag contains 3 red, 4 black and 2 white balls. What is the   [#permalink] 16 Jul 2016, 11:45
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