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.

what adds to 6?

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.

An interesting way to go about this is to use a generating function.



The outside exponent is the number of dice rolled.

Look at the coefficient of the 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:

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.

Well, but that's not it. galactus already gave the answer... :rolleyes:

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.

What is the probability of not rolling a number greater than 4 on a regular dice

1/3 2/3 1/6 1/7

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.

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?