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

 It is currently 25 Apr 2019, 19:06

### 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

# What is the probability of getting a sum of 12 when rolling

Author Message
TAGS:

### Hide Tags

Intern
Joined: 09 Aug 2006
Posts: 6
What is the probability of getting a sum of 12 when rolling  [#permalink]

### Show Tags

Updated on: 23 Feb 2014, 23:58
4
14
00:00

Difficulty:

95% (hard)

Question Stats:

53% (02:53) correct 47% (02:33) wrong based on 425 sessions

### HideShow timer Statistics

What is the probability of getting a sum of 12 when rolling 3 dice simultaneously?

A. 10/216
B. 12/216
C. 21/216
D. 23/216
E. 25/216

Originally posted by anhlukas on 16 Aug 2006, 12:22.
Last edited by Bunuel on 23 Feb 2014, 23:58, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
CEO
Joined: 20 Nov 2005
Posts: 2746
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008

### Show Tags

16 Aug 2006, 15:11
10
8
Sum of 12 can be achieved in following ways
6,5,1---Total cases = 3! = 6
6,4,2---Total cases = 3!= 6
6,3,3---Total cases = 3!/2! = 3
5,5,2---Total cases = 3!/2! = 3
5,4,3---Total cases = 3! = 6
4,4,4---Total cases = 3!/3! = 1

Total cases = 25

Probability = 25 * (1/6 * 1/6 * 1/6) = 25/216
_________________
SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008
##### General Discussion
Director
Joined: 06 May 2006
Posts: 748

### Show Tags

16 Aug 2006, 13:41
4
1
I broke my head 15 minutes on it, then the soln is so devilishly simple!

Basically, if the numbers on two of the dice are decided, then there is only one value of the third die that is possible. So you have to find only those combinations of two dice that yield a sum of 6 or above. e.g. If the value on the 1st die is 1, then you have two possible outcomes - 5 or 6 on the 2nd die. Similarly, for a value of 2 on the first die, you have 3 possible outcomes (4, 5, 6) and so on... However, if you get a value of 6 on the first die, then you can have only 5 possible outcomes.

The total number of outcomes comes out to be (2 + 3 + 4 + 5 + 6 + 5) = 25.

Probability is 25/216!
_________________
Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?
Manager
Joined: 22 Jan 2014
Posts: 173
WE: Project Management (Computer Hardware)
Re: What is the probability of getting a sum of 12 when rolling  [#permalink]

### Show Tags

23 Mar 2015, 04:47
1
anhlukas wrote:
What is the probability of getting a sum of 12 when rolling 3 dice simultaneously?

A. 10/216
B. 12/216
C. 21/216
D. 23/216
E. 25/216

let the dices be a,b,c

a+b+c = 12

but 0 < a,b,c < 6

so we can re-write the equation as

(6-a)+(6-b)+(6-c) = 12
=> a+b+c = 6
which has total of C(8,2) whole number solutions = 28
but out of these 28, three cases must be where 2 of a,b, or c is 0 and the other is 6. so we need to remove those cases which would be 3 cases ( C(3,2) )
so total 25 such cases

_________________
Illegitimi non carborundum.
Intern
Joined: 11 Jan 2015
Posts: 2
GPA: 3.3
Re: What is the probability of getting a sum of 12 when rolling  [#permalink]

### Show Tags

04 Apr 2015, 13:48
I think it is very easy...........
Start checking from the smaller or bigger numbers on the dice. We will check from bigger numbers working downwards: start with 6, it has the following options: (6,5,1), (6,4,2), (6,3,3). Now pass on to 5: (5,5,2), (5,4,3). Now 4: (4,4,4). And that’s it, these are all number combinations that are possible, if you go on to 3, you will notice that you need to use 4, 5 or 6, that you have already considered (the same goes for 2 and 1). Now analyze every option: 6,5,1 has 6 options (6,5,1), (6,1,5), (5,1,6), (5,6,1), (1,6,5), (1,5,6). So do (6,4,2) and (5,4,3). Options (6,3,3) and (5,5,2) have 3 options each: (5,5,2), (5,2,5) and (2,5,5). The same goes for (6,3,3). The last option (4,4,4) has only one option. The total is 3*6+2*3+1=18+6+1 = 25 out of 216 (6x6x6) options.

5,5,2= (552),(255),(525)
Like= 336
Intern
Joined: 06 Oct 2014
Posts: 11
Concentration: Finance
GMAT 1: 700 Q45 V41
GPA: 3.8
What is the probability of getting a sum of 12 when rolling  [#permalink]

### Show Tags

25 Aug 2015, 13:56
An easy way to visualise it is by drawing a Binomial tree, we've all done those in school and if each branch has a 1/2 probability, you'll find that there's only 3 ways to get there.

(1/2)^3 x 3 = 3/8

Hope it helps!

G
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9146
Location: Pune, India
Re: What is the probability of getting a sum of 12 when rolling  [#permalink]

### Show Tags

25 Aug 2015, 22:25
3
1
anhlukas wrote:
What is the probability of getting a sum of 12 when rolling 3 dice simultaneously?

A. 10/216
B. 12/216
C. 21/216
D. 23/216
E. 25/216

Check out these two posts:

http://www.veritasprep.com/blog/2012/10 ... l-picture/
http://www.veritasprep.com/blog/2012/10 ... e-part-ii/

They discuss a shortcut to "how to find the probability of obtaining a given sum when 3 dice are rolled"
_________________
Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 06 Oct 2013
Posts: 45
Re: What is the probability of getting a sum of 12 when rolling  [#permalink]

### Show Tags

20 Sep 2015, 11:05
VeritasPrepKarishma wrote:
Check out these two posts:

http://www.veritasprep.com/blog/2012/10 ... l-picture/
http://www.veritasprep.com/blog/2012/10 ... e-part-ii/

They discuss a shortcut to "how to find the probability of obtaining a given sum when 3 dice are rolled"

Excellent!!! Thanks Karishma
Intern
Joined: 21 Oct 2015
Posts: 1
Re: What is the probability of getting a sum of 12 when rolling  [#permalink]

### Show Tags

24 Nov 2015, 06:59
Thanks Karishma,

Could you please explain how 9 is calculated that is subtracted from 9C2 in below scenario?

Similarly, how will you adjust for the sum of 10? There will be cases where the split is like this: (7, 0, 0) or (6, 1, 0). These do not work since the maximum a die can show is 6. So you need to remove 9 cases (3 arrangements of 7, 0, 0 and 6 arrangements of 6, 1, 0)
Senior Manager
Joined: 03 Apr 2013
Posts: 274
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: What is the probability of getting a sum of 12 when rolling  [#permalink]

### Show Tags

09 Jul 2017, 02:53
thefibonacci wrote:
anhlukas wrote:
What is the probability of getting a sum of 12 when rolling 3 dice simultaneously?

A. 10/216
B. 12/216
C. 21/216
D. 23/216
E. 25/216

let the dices be a,b,c

a+b+c = 12

but 0 < a,b,c < 6

so we can re-write the equation as

(6-a)+(6-b)+(6-c) = 12
=> a+b+c = 6
which has total of C(8,2) whole number solutions = 28
but out of these 28, three cases must be where 2 of a,b, or c is 0 and the other is 6. so we need to remove those cases which would be 3 cases ( C(3,2) )
so total 25 such cases

I understand using this method and have used. But here I didn't understand the rewriting the equation part. Please explain that and what follows that. Bunuel, if possible, would be great if you could help me out here.
_________________
Spread some love..Like = +1 Kudos
Re: What is the probability of getting a sum of 12 when rolling   [#permalink] 09 Jul 2017, 02:53
Display posts from previous: Sort by