Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 23 Feb 2014
Posts: 34
GMAT 1: 560 Q41 V26 GMAT 2: 610 Q46 V28

Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
Updated on: 09 Jul 2017, 02:36
Question Stats:
74% (00:43) correct 26% (00:53) wrong based on 168 sessions
HideShow timer Statistics
Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8. A. 1/12 B. 1/11 C. 1/9 D. 5/36 E. 1/6 I am struggling to understand a concept  This seems like an error in MGMAT book  But i want to get it clarified and get a better understanding. The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8. The Concern/Error: The successful outcomes is being counted as 26, 35,44, 53, 62. I think there needs to be another 44 that should be counted. Because 4 in Dice 1 is different from 4 in dice 2. Can someone please explain? Anyone facing same issue?
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by vingmat001 on 02 Mar 2014, 20:20.
Last edited by Bunuel on 09 Jul 2017, 02:36, edited 2 times in total.
Renamed the topic and edited the question.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8278
Location: Pune, India

Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
02 Mar 2014, 22:22
vingmat001 wrote: I am struggling to understand a concept  This seems like an error in MGMAT book  But i want to get it clarified and get a better understanding. The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8. The Concern/Error: The successful outcomes is being counted as 26, 35,44, 53, 62. I think there needs to be another 44 that should be counted. Because 4 in Dice 1 is different from 4 in dice 2. Can someone please explain? Anyone facing same issue? Say one die is red in color and the other is yellow. Why do we take two cases (2, 6) and (6, 2)? Because a 2 on the red one and 6 on the yellow one is different from 2 on the yellow one and 6 on the red one. In the case of (4, 4), you have 4 on the red one and 4 on the yellow one. How can you have another (4, 4) case? The other one will also be 4 on the red one and 4 on the yellow one.
_________________
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 >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 23 Feb 2014
Posts: 34
GMAT 1: 560 Q41 V26 GMAT 2: 610 Q46 V28

Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
03 Mar 2014, 16:30
Wow !! Thanks for the explanation Karishma! Just add color to the dice and it all becomes clear.



Intern
Joined: 04 Jan 2014
Posts: 3
Location: Canada
Concentration: Finance, Strategy
GMAT Date: 07312014
GPA: 3.95
WE: Engineering (Energy and Utilities)

Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
03 Mar 2014, 22:47
vingmat001 wrote: I am struggling to understand a concept  This seems like an error in MGMAT book  But i want to get it clarified and get a better understanding. The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8. The Concern/Error: The successful outcomes is being counted as 26, 35,44, 53, 62. I think there needs to be another 44 that should be counted. Because 4 in Dice 1 is different from 4 in dice 2. Can someone please explain? Anyone facing same issue? Another way to visualize this problem is as shown in the attached diagram. In the test, you do not need to list all possible sums. Just look for the one you are interested in and count them.
Attachments
File comment: Probability of getting a defined sum from the sum of the numbers on two faces of a randomly rolled cube.
2 rolled cubes numbered 1 to 6.docx [58.01 KiB]
Downloaded 141 times



Intern
Joined: 24 Feb 2017
Posts: 38

Basic conceptual question in probability
[#permalink]
Show Tags
08 Jul 2017, 19:01
"Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?" ( MGMAT example question Guide 5 Chapter 4) We all know the right way solve this question, which is  Total outcomes 36, Desirable outcomes 5. So, Probability is 5/36. My question  why is the # of total outcomes not 11? Why are we considering the total outcomes of dierolls, and not the total outcomes of the sum. If I consider the total outcomes of the sum = 2 to 12 then my probability is 1/11 Again, I completely understand that the right answer takes into effect the higher number of individual outcomes as below. Sum # outcomes 2 1 3 2 4 3 . . .... 11 2 12 1 My question is what makes the solution of 1/11 wrong? Does it depend on what we define as an "outcome"?



Director
Joined: 05 Mar 2015
Posts: 984

Re: Basic conceptual question in probability
[#permalink]
Show Tags
08 Jul 2017, 20:41
rbramkumar wrote: "Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?" ( MGMAT example question Guide 5 Chapter 4) We all know the right way solve this question, which is  Total outcomes 36, Desirable outcomes 5. So, Probability is 5/36. My question  why is the # of total outcomes not 11? Why are we considering the total outcomes of dierolls, and not the total outcomes of the sum. If I consider the total outcomes of the sum = 2 to 12 then my probability is 1/11 Again, I completely understand that the right answer takes into effect the higher number of individual outcomes as below. Sum # outcomes 2 1 3 2 4 3 . . .... 11 2 12 1 My question is what makes the solution of 1/11 wrong? Does it depend on what we define as an "outcome"? number of ways u get 8 2,6 6,2 3,5 5,3 4,4 = 5ways and total possible outcomes of two dice = 6*6=36 thus probability = 5/36....



Intern
Joined: 24 Feb 2017
Posts: 38

Re: Basic conceptual question in probability
[#permalink]
Show Tags
09 Jul 2017, 00:55
Sorry, I don't think you read my question right. Anyway, thanks for your input.



BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 3128
Location: India
GPA: 3.12

Re: Basic conceptual question in probability
[#permalink]
Show Tags
09 Jul 2017, 01:22
rbramkumar wrote: "Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?" ( MGMAT example question Guide 5 Chapter 4) We all know the right way solve this question, which is  Total outcomes 36, Desirable outcomes 5. So, Probability is 5/36. My question  why is the # of total outcomes not 11? Why are we considering the total outcomes of dierolls, and not the total outcomes of the sum. If I consider the total outcomes of the sum = 2 to 12 then my probability is 1/11Again, I completely understand that the right answer takes into effect the higher number of individual outcomes as below. Sum # outcomes 2 1 3 2 4 3 . . .... 11 2 12 1 My question is what makes the solution of 1/11 wrong? Does it depend on what we define as an "outcome"? Since there are 1 outcome for getting sum of 2 and this pattern increases till 7(where the number of outcomes is 6) The maximum outcomes happen, when the sum if 7 {(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)} and then the outcomes reduce till we reach 12 as sum, where the number of outcomes is 1(6,6) The probability of an event happening = \(\frac{P(A)}{P(T)}\) where P(A) = Possibility_of_an_event_happening and P(T) = Total_number_of_outcomes Here the Possibility of getting 8 is 5 {(2,6),(3,5),(4,4),(5,3),(6,2)} Total possibilities are 1+2+3+4+5+6+5+4+3+2+1 = 36. Thats why the probability is 5/36 and not 1/11 as your had asked. Hope that helps!
_________________
You've got what it takes, but it will take everything you've got



Math Expert
Joined: 02 Sep 2009
Posts: 49206

Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
09 Jul 2017, 02:46
rbramkumar wrote: "Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that the sum of the rolls is 8?" ( MGMAT example question Guide 5 Chapter 4) We all know the right way solve this question, which is  Total outcomes 36, Desirable outcomes 5. So, Probability is 5/36. My question  why is the # of total outcomes not 11? Why are we considering the total outcomes of dierolls, and not the total outcomes of the sum. If I consider the total outcomes of the sum = 2 to 12 then my probability is 1/11 Again, I completely understand that the right answer takes into effect the higher number of individual outcomes as below. Sum # outcomes 2 1 3 2 4 3 . . .... 11 2 12 1 My question is what makes the solution of 1/11 wrong? Does it depend on what we define as an "outcome"? Merging topics. I think pushpitkc answers your question but just to make sure you understand. Not all sums out of 11 have the same number of occurrences. The sum of 2 can occur in 1 way  (1, 1) but the sum of two can occur in 2 way  (1, 2) and (2, 1). Hope it helps.
_________________
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? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 24 Feb 2017
Posts: 38

Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
09 Jul 2017, 05:19
Thank you, pushpitkc and bunuel.
I understand the concept of "# on dice 1, # on dice 2" as an outcome, but was merely speculating how the answer looked like when we look at "SUM" as an outcome.
Let me elaborate my thoughts:
Former: Outcome (# on dice1, # on dice 2) Total outcomes 36
Latter: Outcome is defined as the "Sum" of the #s in 2 dices Total outcomes 11
I was getting derailed by the fact that the # Total outcomes needed to be 11, but I think the latter definition of "outcome" changes the basic assumption in Probability questions, i.e., equally likely outcomes (no bias). I missed the fact that this is a probability distribution where we (sum the area of desired/sum the total area under histogram) to get to the required probability. This seems to result in the original answer of 5/36.
There's really no need to think in the latter manner, just trying out different ways. Thanks and all the best!



Intern
Joined: 11 Sep 2012
Posts: 5

Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
17 Oct 2017, 05:20
VeritasPrepKarishma wrote: vingmat001 wrote: I am struggling to understand a concept  This seems like an error in MGMAT book  But i want to get it clarified and get a better understanding. The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8. The Concern/Error: The successful outcomes is being counted as 26, 35,44, 53, 62. I think there needs to be another 44 that should be counted. Because 4 in Dice 1 is different from 4 in dice 2. Can someone please explain? Anyone facing same issue? Say one die is red in color and the other is yellow. Why do we take two cases (2, 6) and (6, 2)? Because a 2 on the red one and 6 on the yellow one is different from 2 on the yellow one and 6 on the red one. In the case of (4, 4), you have 4 on the red one and 4 on the yellow one. How can you have another (4, 4) case? The other one will also be 4 on the red one and 4 on the yellow one. Hi, I can understand why in the "total number of desired outcome" we count only 1 combination {4;4} However, in the "total number of possible outcome" we put 36 = 6*6. This number include all the duplicated {1;1}, {2,2}.... {6,6}; Otherwise we don't have 36, we only have 30 = 6*5 possible outcome. May someone please help? Thank you!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8278
Location: Pune, India

Re: Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
17 Oct 2017, 21:39
phanthibaovien wrote: VeritasPrepKarishma wrote: vingmat001 wrote: I am struggling to understand a concept  This seems like an error in MGMAT book  But i want to get it clarified and get a better understanding. The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8. The Concern/Error: The successful outcomes is being counted as 26, 35,44, 53, 62. I think there needs to be another 44 that should be counted. Because 4 in Dice 1 is different from 4 in dice 2. Can someone please explain? Anyone facing same issue? Say one die is red in color and the other is yellow. Why do we take two cases (2, 6) and (6, 2)? Because a 2 on the red one and 6 on the yellow one is different from 2 on the yellow one and 6 on the red one. In the case of (4, 4), you have 4 on the red one and 4 on the yellow one. How can you have another (4, 4) case? The other one will also be 4 on the red one and 4 on the yellow one. Hi, I can understand why in the "total number of desired outcome" we count only 1 combination {4;4} However, in the "total number of possible outcome" we put 36 = 6*6. This number include all the duplicated {1;1}, {2,2}.... {6,6}; Otherwise we don't have 36, we only have 30 = 6*5 possible outcome. May someone please help? Thank you! These are the 36 cases: {1, 1}, {1, 2}, {1, 3}, {1, 4}, {1, 5}, {1, 6} {2, 1}, {2, 2}, {2, 3}, {2, 4}, {2, 5}, {2, 6} {3, 1}, {3, 2}, {3, 3}, {3, 4}, {3, 5}, {3, 6} {4, 1}, {4, 2}, {4, 3}, {4, 4}, {4, 5}, {4, 6} {5, 1}, {5, 2}, {5, 3}, {5, 4}, {5, 5}, {5, 6} {6, 1}, {6, 2}, {6, 3}, {6, 4}, {6, 5}, {6, 6}
_________________
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 >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Senior Manager
Joined: 14 Oct 2015
Posts: 252
GPA: 3.57

Two number cubes with faces numbered 1 to 6 are rolled. What is the
[#permalink]
Show Tags
27 Jan 2018, 17:30
vingmat001 wrote: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8. A. 1/12 B. 1/11 C. 1/9 D. 5/36 E. 1/6 I am struggling to understand a concept  This seems like an error in MGMAT book  But i want to get it clarified and get a better understanding. The questions is: Two number cubes with faces numbered 1 to 6 are rolled. What is the probability that that sum of the rolls is 8. The Concern/Error: The successful outcomes is being counted as 26, 35,44, 53, 62. I think there needs to be another 44 that should be counted. Because 4 in Dice 1 is different from 4 in dice 2. Can someone please explain? Anyone facing same issue? Here is an alternate approach. We choose 1 dice and individually calculate the possibility that it will make a sum of 8 when combined with a number in the 2nd dice. If the first dice rolls a... 1: \(\frac{0}{6}\) possibility of it making a sum of 8 when combined with a number in the second dice. 2: \(\frac{1}{6}\) chance (need 6 on the second dice) it will make a sum of 8. 3: \(\frac{1}{6}\) chance (need 5 on the second dice) it will make a sum of 8. 4: \(\frac{1}{6}\) chance (need 4 on the second dice) it will make a sum of 8. 5: \(\frac{1}{6}\) chance (need 3 on the second dice) it will make a sum of 8. 6: \(\frac{1}{6}\) chance (need 2 on the second dice) it will make a sum of 8. Each digit in the first dice makes 6 combinations (one with each digit in second dice) and added up, they all make 36 combinations. So each digit's weight or contribution in total probability is 1/6. Adding probability sums. \(\frac{0}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6} + \frac{1}{6}*\frac{1}{6}\) \(= 0 + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} + \frac{1}{36} = \frac{5}{36}\) It is important to understand that of the 6 digits on a dice, only 5 make a combination that sums up to 8. The digit 1 cannot possibly add up to make 8 as the maximum digit in the second dice is 6 which would make the sum 7.
_________________
Please hit Kudos if this post helped you inch closer to your GMAT goal. Procrastination is the termite constantly trying to eat your GMAT tree from the inside. There is one fix to every problem, working harder!




Two number cubes with faces numbered 1 to 6 are rolled. What is the &nbs
[#permalink]
27 Jan 2018, 17:30






