When two fair dice are rolled, why are doubles not included twice in a table of possible events

Question

In conditional probability I'm asked to answer the question:

If two fair dice are​ rolled, find the probability that the sum of the dice is $8$​, given that the sum is greater than $3$.

I have been getting them wrong because when finding the number of events that the sum equals $8$. I count $\{4,4\}$ twice, but in a table of events its only listed once. That doesn't make sense to me because they do count $\{2,6\},\{6,2\},\{3,5\},\{5,3\}$. So why not $\{4,4\},\{4,4\}$?

Thanks.
Spencer

Answer 1

There is only one possible way to throw $\{4,4\}$ with two dices, your first dice should be $4$ and your second dice should be $4$. To throw the combination $\{2,6\}$ we have two possibilities, your first dice should can be $2$ or $6$, and your second dice should then be respectively $6$ or $2$. Does this help?