# if you roll a pair of dice, what is the probability of rolling a sum of 6?

if you roll a pair of dice, what is the probability of rolling a sum of 6?

 eawoodall Posts: 232, Reputation: 48 Full Member #2 Oct 25, 2010, 03:27 PM
Quote:
 Originally Posted by Mundo5 if you roll a pair of dice, what is the probability of rolling a sum of 6?
quantum algebra states that separate events must be counted separately.
think of the dice as having two colors. One is red. One is blue.
make a table with the order red, blue.
the possible results are 36 possibilities.
you can get a 1 through 6 on the red die, and 1-6 on the blue.

1+5=6.
5+1=6.
2+4=6.
4+2=6.
3+3=6.

so we have 5 total possibilities out of 36.

note
again the only possible results of the dice roll are:
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

so there is only one 3,3 most people mess up when they do not realize the events are quantum. And think there are 6 results for 6 total but there are only 5.
 galactus Posts: 2,272, Reputation: 1436 Ultra Member #3 Oct 25, 2010, 03:50 PM

$\left(\sum_{k=1}^{6}x^{k}\right)^{2}=x^{2}+2x^{3}+ 3x^{4}+4x^{5}+5x^{6}+....+x^{12}$

The outside exponent is the number of dice rolled.

Look at the coefficient of the $x^{6}$ term.
It is 5. Thus, there are 5 possible ways to roll a sum of 6.

This is overkill with only two dice because there are 36 outcomes in all and one can simply count the rolls that sum to 6.

But, say the problem stated, "You roll 5 dice. what is the probability of getting a sum of 24?".

Then, it is more difficult and the GF comes in handy.

Another way to think of it is to note that in order to roll a sum of 6, the first roll has to be a 1,2,3,4,5. This can happen with probability 5/6.
Therefore, the next roll, say, for the 1, has to be a 5. For the first roll of a 2, the next roll has to be a 4. And so on. So, the probability of getting the number we need is 1/6. There are 36 outcomes, so we have:

$36\cdot \frac{5}{6}\cdot \frac{1}{6}=5$
 tmeunknown Posts: 44, Reputation: -1 Junior Member #4 Nov 1, 2010, 12:18 PM
There are only three possible ways of getting a sum of six, they are 1 and 5, 2 and 4, 3 and 3. Three out of 36 possible combination's... 8.3 pecent chance of getting a sum of six.
eawoodall (Nov 1, 2010 02:15 PM): read my post of all posible results - eawoodall   Source:
 tmeunknown Posts: 44, Reputation: -1 Junior Member #5 Nov 1, 2010, 12:19 PM
Comment on tmeunknown's post
Quote:
 Originally Posted by tmeunknown There are only three possible ways of getting a sum of six, they are 1 and 5, 2 and 4, 3 and 3. Three out of 36 possible combination's... 8.3 pecent chance of getting a sum of six.
If your only using the possible ways once.
 Unknown008 Posts: 8,147, Reputation: 3745 Uber Member #6 Nov 1, 2010, 01:07 PM

 galactus Posts: 2,272, Reputation: 1436 Ultra Member #7 Nov 1, 2010, 01:44 PM
There are 5 ways,

1+5=6
5+1=6
3+3=6
4+2=6
2+4=6

You can easily count them up by listing all the 36 possibilites and counting the 5 ways.
 visam Posts: 1, Reputation: 1 New Member #8 Jul 11, 2012, 05:07 AM
What is the probability of not rolling a number greater than 4 on a regular dice

1/3 2/3 1/6 1/7
 ebaines Posts: 10,594, Reputation: 5809 Expert #9 Jul 11, 2012, 06:45 AM
Quote:
 Originally Posted by visam What is the probability of not rolling a number greater than 4 on a regular dice
Count up the number of ways you can get a result less than or equal to 4, and divide by the total number of possible outcomes. Post back with your answer.
 eawoodall Posts: 232, Reputation: 48 Full Member #10 Jul 11, 2012, 11:39 AM
to not roll a number greater than 4, using quantum algebra.

you use a blue colored die.

all possible results are :
1
2
3
4
5
6

how many of those results are not greater than 4?
1
2
3
4

1/6 + 1/6 +1/6 +1/6 are the quantum results of each as probability.
or 4/6 times you would get a result not greater than 4.
some people would reduce that to 2/3, but 4/6 is more instructive.

p.s. also note I answered on oct 25th,2010 the last question correctly, but some people think that a person who read my answer on nov 1,2010 gave the first right answer? How can you not know oct 25,2010 comes before nov 1st,2010?

Quote:
 Originally Posted by visam What is the probability of not rolling a number greater than 4 on a regular dice 1/3 2/3 1/6 1/7

## Check out some similar questions!

What is the travel of a rolling offset with a roll of 33 5/8 in. and a set of 32 1/4 in.

Just a quick question.

Dice Probability [ 3 Answers ]

Suppose you roll 4 dice. a) What is the probability that you get 4 different numbers? b) What is the probability that you get '2 pairs' (two of one number and two of another number?) c) Now suppose that you continue rolling 4 dice over and over until you get either get '4 different...

Dice probability [ 1 Answers ]

Dice

Probability for dice roll outcomes [ 2 Answers ]

I have searched for similar answers with no luck so I am hoping one of you can be kind enough to help me with this. Using standard 6 sided die - all results should be based on only one roll for each question of the following number of die. Each question below is independent of other questions,...