Last visit was: 25 Apr 2026, 02:05 It is currently 25 Apr 2026, 02:05
Home
Messages
Tests
Schools
Events
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
lucalelli88
User avatar
Joined: 23 Dec 2009
Last visit: 13 Mar 2010
Posts: 14
Own Kudos:
219
 [3]
Given Kudos: 7
Posts: 14
Kudos: 219
 [3]
When 2 fair dice are rolled what is the probability of having 6 as sum 16 Jan 2010, 02:42
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

25% (medium)

Question Stats:

70% (00:53) correct 30% (01:06) wrong based on 179 sessions

History

Date
Time
Result
Not Attempted Yet
When 2 fair dice are rolled what is the probability of having 6 as sum of the resulting numbers?

A 1/12
B 1/6
C 5/6
D 5/36
E 1/2
ShowHide Answer
Official Answer
D
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,127
 [3]
Given Kudos: 105,878
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,822
Kudos: 811,127
 [3]
When 2 fair dice are rolled what is the probability of having 6 as sum 16 Jan 2010, 03:02
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
lucalelli88
when 2 fair dice are rolled what is the probability of having 6 as sum of the resulting numbers?
A 1/12
B 1/6
C 5/6
D 5/36
E 1/2

can you solve it.... because i got an answer but i cannot understand why it is wrong.
Show more

There are 36 possible outcomes when a pair of dice is rolled (6 for the first die X 6 for the second one). From this 36 outcomes five have a total of 6, {(1,5), (5,1), (2,4), (4,2), (3,3)}, hence the probability of the two numbers adding up to 6 is \(\frac{5}{36}\).

Answer: D.
User avatar
lucalelli88
User avatar
Joined: 23 Dec 2009
Last visit: 13 Mar 2010
Posts: 14
Own Kudos:
219
 [1]
Given Kudos: 7
Posts: 14
Kudos: 219
 [1]
When 2 fair dice are rolled what is the probability of having 6 as sum 16 Jan 2010, 03:41
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
i have choosen 1/6 cuz I have thought that there are 6 possible outcomes 5,1 1,5 4,2 2,4 3,3 and again 3,3 because 3,3 can happen 2 times...
why dont you count 3,3 2 times?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,127
 [1]
Given Kudos: 105,878
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,822
Kudos: 811,127
 [1]
When 2 fair dice are rolled what is the probability of having 6 as sum 16 Jan 2010, 04:36
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
lucalelli88
i have choosen 1/6 cuz I have thought that there are 6 possible outcomes 5,1 1,5 4,2 2,4 3,3 and again 3,3 because 3,3 can happen 2 times...
why dont you count 3,3 2 times?
Show more

When we count (4,2) and (2,4), it means that we get: 4 on die #1 and 2 on die #2 in first case and 2 on dies #1 and 4 on die #2 in the second case.

With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.
User avatar
lucalelli88
User avatar
Joined: 23 Dec 2009
Last visit: 13 Mar 2010
Posts: 14
Own Kudos:
219
Given Kudos: 7
Posts: 14
Kudos: 219
When 2 fair dice are rolled what is the probability of having 6 as sum 16 Jan 2010, 06:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
thank you... my approach was wrong! KUDOS FOR YOU!


Bunuel
lucalelli88
i have choosen 1/6 cuz I have thought that there are 6 possible outcomes 5,1 1,5 4,2 2,4 3,3 and again 3,3 because 3,3 can happen 2 times...
why dont you count 3,3 2 times?

When we count (4,2) and (2,4), it means that we get: 4 on die #1 and 2 on die #2 in first case and 2 on dies #1 and 4 on die #2 in the second case.

With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.
Show more
User avatar
frank1
User avatar
Joined: 24 Apr 2010
Last visit: 11 Dec 2010
Posts: 42
Own Kudos:
24
Posts: 42
Kudos: 24
When 2 fair dice are rolled what is the probability of having 6 as sum 12 Aug 2010, 19:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.
Show more
well bit confused....
i think it means it is not times ie 1 time and 2nd time rather it is in 1st dice and in second dice...
but suppose if die we colored green and blue
would it be like
3 on G ,3 on B and 3 on B ,3 on G?

Can you please clarify?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,127
Given Kudos: 105,878
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,822
Kudos: 811,127
When 2 fair dice are rolled what is the probability of having 6 as sum 13 Aug 2010, 03:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
frank1
Bunuel
With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.
well bit confused....
i think it means it is not times ie 1 time and 2nd time rather it is in 1st dice and in second dice...
but suppose if die we colored green and blue
would it be like
3 on G ,3 on B and 3 on B ,3 on G?

Can you please clarify?
Show more

Not sure I understood your question...

There are only following 5 cases possible to have sum of 6:

#1|#2
1---5
2---4
3---3
4---2
5---1

Do we have any other case? It doesn't matter whether dice are colored, they are already numbered. (3,3) means 3 on die #1 and 3 on die #2 (3 on die #2 and 3 on die #1 is basically the same case).
User avatar
nkimidi7y
User avatar
Joined: 09 Apr 2012
Last visit: 25 Apr 2019
Posts: 47
Own Kudos:
233
Given Kudos: 29
Posts: 47
Kudos: 233
When 2 fair dice are rolled what is the probability of having 6 as sum 14 Aug 2017, 03:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
frank1
Bunuel
With (3,3) we have only one case: 3 on #1 die and 3 on #2 die, there is no case two.

Hope it's clear.
well bit confused....
i think it means it is not times ie 1 time and 2nd time rather it is in 1st dice and in second dice...
but suppose if die we colored green and blue
would it be like
3 on G ,3 on B and 3 on B ,3 on G?

Can you please clarify?

Not sure I understood your question...

There are only following 5 cases possible to have sum of 6:

#1|#2
1---5
2---4
3---3
4---2
5---1

Do we have any other case? It doesn't matter whether dice are colored, they are already numbered. (3,3) means 3 on die #1 and 3 on die #2 (3 on die #2 and 3 on die #1 is basically the same case).
Show more

In such a case,
1,1 2,2 3,3 4,4 5,5 and 6,6 will be the same.

So our possible outcomes are just 30.

Our answer would then be 1/6.

Am i missing something?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 25 Apr 2026
Posts: 109,822
Own Kudos:
811,127
Given Kudos: 105,878
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,822
Kudos: 811,127
When 2 fair dice are rolled what is the probability of having 6 as sum 14 Aug 2017, 03:48
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nkimidi7y

1,1 2,2 3,3 4,4 5,5 and 6,6 will be the same.

So our possible outcomes are just 30.

Our answer would then be 1/6.

Am i missing something?
Show more

No, there are till 36 cases:

(1, 1)
(1, 2)
...
(1, 6)
6 cases.

(2, 1)
(2, 2)
...
(2, 6)
6 cases.

(3, 1)
(3, 2)
...
(3, 6)
6 cases.

(4, 1)
(4, 2)
...
(4, 6)
6 cases.

(5, 1)
(5, 2)
...
(5, 6)
6 cases.

(6, 1)
(6, 2)
...
(6, 6)
6 cases.

6*6 = 36.
User avatar
jedit
User avatar
Joined: 14 Oct 2015
Last visit: 07 Sep 2021
Posts: 201
Own Kudos:
387
 [2]
Given Kudos: 854
Schools: Stanford '20 HBS '20 Sloan '20
GPA: 3.57
Products:
My Reviews
Schools: Stanford '20 HBS '20 Sloan '20
Posts: 201
Kudos: 387
 [2]
When 2 fair dice are rolled what is the probability of having 6 as sum 15 Aug 2017, 06:36
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
nkimidi7y


In such a case,
1,1 2,2 3,3 4,4 5,5 and 6,6 will be the same.

So our possible outcomes are just 30.

Our answer would then be 1/6.

Am i missing something?
Show more


Don't think of it like combination choices where you can flip and come up with the same thing. Think of 36 possibilities in 6 groups where first roll is 1 for all pairs in row 1, 2 for all pairs in row 2 and so on. You have 5 bold faced choices that have sum 6. Every row starting 1-5 has one matching pair where sum is 6, but the last row starting with 6 cannot come up with any second dice roll number to get to a sum of 6. So we only have 5 of 36 choices that have a sum of 6.

11,12, 13,14,15,16
21,22,23,24,25,26
31,32,33,34,35,36
41,42,43,44,45,46
51,52,53,54,55,56
61,62,63,64,65,66
User avatar
BrushMyQuant
User avatar
Joined: 05 Apr 2011
Last visit: 03 Apr 2026
Posts: 2,286
Own Kudos:
2,680
Given Kudos: 100
Status:Tutor - BrushMyQuant
Location: India
Concentration: Finance, Marketing
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
GPA: 3
WE:Information Technology (Computer Software)
Expert
Expert reply
Schools: XLRI (A)
GMAT 1: 700 Q51 V31
Posts: 2,286
Kudos: 2,680
When 2 fair dice are rolled what is the probability of having 6 as sum Updated on: 19 Jun 2024, 05:01
Originally posted by BrushMyQuant on 08 Oct 2022, 10:26.
Last edited by BrushMyQuant on 19 Jun 2024, 05:01, edited 1 time in total.
Kudos
Add Kudos
Bookmarks
Bookmark this Post
↧↧↧ Detailed Video Solution to the Problem ↧↧↧


Given that 2 fair dice are rolled and we need to find what is the probability of having 6 as sum of the resulting numbers?

As we are rolling two dice => Number of cases = \(6^2\) = 36

Lets start writing the possible cases where sum of the two rolls = 6. Following are the possible cases:
(1,5)
(2,4)
(3,3)
(4,2)
(5,1)

=> 5 cases

=> Probability that sum of two rolls is 6 = \(\frac{5}{36}\)

So, Answer will be D
Hope it helps!

Watch the following video to learn How to Solve Dice Rolling Probability Problems

­
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,977
Own Kudos:
1,117
Posts: 38,977
Kudos: 1,117
When 2 fair dice are rolled what is the probability of having 6 as sum 17 Feb 2024, 03:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderators:
Bunuel
Math Expert
109822 posts
Krunaal
Tuck School Moderator
853 posts