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

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Intern
Joined: 23 Dec 2009
Posts: 21
When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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16 Jan 2010, 02:42
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68% (00:55) correct 32% (01:05) wrong based on 136 sessions

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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
Math Expert
Joined: 02 Sep 2009
Posts: 54367
Re: When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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16 Jan 2010, 03:02
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 $$\frac{5}{36}$$.

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

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16 Jan 2010, 03:41
1
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?
Math Expert
Joined: 02 Sep 2009
Posts: 54367
Re: When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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16 Jan 2010, 04:36
1
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.
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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16 Jan 2010, 06:35
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.
Manager
Joined: 24 Apr 2010
Posts: 55
Re: When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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12 Aug 2010, 19:43
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?

Math Expert
Joined: 02 Sep 2009
Posts: 54367
Re: When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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13 Aug 2010, 03:03
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).
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Posts: 56
Re: When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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14 Aug 2017, 03:34
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?
Math Expert
Joined: 02 Sep 2009
Posts: 54367
Re: When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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14 Aug 2017, 03:48
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.
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Posts: 249
GPA: 3.57
Re: When 2 fair dice are rolled what is the probability of having 6 as sum  [#permalink]

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15 Aug 2017, 06:36
1
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
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Re: When 2 fair dice are rolled what is the probability of having 6 as sum   [#permalink] 15 Aug 2017, 06:36
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