It is currently 16 Dec 2017, 20:27

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# When 2 fair dice are rolled what is the probability of having 6 as sum

Author Message
TAGS:

### Hide Tags

Intern
Joined: 23 Dec 2009
Posts: 27

Kudos [?]: 130 [0], given: 7

When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

16 Jan 2010, 01:42
1
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

71% (00:34) correct 29% (00:46) wrong based on 123 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA

Kudos [?]: 130 [0], given: 7

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135880 [0], given: 12715

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

16 Jan 2010, 02:02
Expert's post
2
This post was
BOOKMARKED
lucalelli88 wrote:
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.

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 $$\frac{5}{36}$$.

_________________

Kudos [?]: 135880 [0], given: 12715

Intern
Joined: 23 Dec 2009
Posts: 27

Kudos [?]: 130 [1], given: 7

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

16 Jan 2010, 02:41
1
KUDOS
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?

Kudos [?]: 130 [1], given: 7

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135880 [1], given: 12715

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

16 Jan 2010, 03:36
1
KUDOS
Expert's post
lucalelli88 wrote:
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.
_________________

Kudos [?]: 135880 [1], given: 12715

Intern
Joined: 23 Dec 2009
Posts: 27

Kudos [?]: 130 [0], given: 7

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

16 Jan 2010, 05:35
thank you... my approach was wrong! KUDOS FOR YOU!

Bunuel wrote:
lucalelli88 wrote:
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.

Kudos [?]: 130 [0], given: 7

Manager
Joined: 24 Apr 2010
Posts: 60

Kudos [?]: 10 [0], given: 0

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

12 Aug 2010, 18:43
Bunuel wrote:
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?

Kudos [?]: 10 [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135880 [0], given: 12715

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

13 Aug 2010, 02:03
frank1 wrote:
Bunuel wrote:
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?

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).
_________________

Kudos [?]: 135880 [0], given: 12715

Non-Human User
Joined: 09 Sep 2013
Posts: 14813

Kudos [?]: 288 [0], given: 0

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

14 Aug 2017, 01:06
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.
_________________

Kudos [?]: 288 [0], given: 0

Manager
Joined: 09 Apr 2012
Posts: 63

Kudos [?]: 68 [0], given: 29

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

14 Aug 2017, 02:34
Bunuel wrote:
frank1 wrote:
Bunuel wrote:
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?

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).

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?

Kudos [?]: 68 [0], given: 29

Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135880 [0], given: 12715

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

14 Aug 2017, 02:48
nkimidi7y wrote:
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?

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.
_________________

Kudos [?]: 135880 [0], given: 12715

Manager
Joined: 14 Oct 2015
Posts: 222

Kudos [?]: 97 [1], given: 487

Re: When 2 fair dice are rolled what is the probability of having 6 as sum [#permalink]

### Show Tags

15 Aug 2017, 05:36
1
KUDOS
nkimidi7y wrote:

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?

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
_________________

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!

Kudos [?]: 97 [1], given: 487

Re: When 2 fair dice are rolled what is the probability of having 6 as sum   [#permalink] 15 Aug 2017, 05:36
Display posts from previous: Sort by