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• ### $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 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, 11:39 3 34 00:00 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 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 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. _________________ ##### General Discussion Senior Manager 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 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 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, 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 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 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 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 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 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 Joined: 20 Jan 2014 Posts: 144 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, 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 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 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 Joined: 14 Aug 2017 Posts: 42 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, 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 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 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 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 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 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 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
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