If we temporarily consider the dice to be distinct (say one is red and one is blue, or call one dice one and the other dice two) then there are 36 possible outcomes. Since we are only interested in the sum of the pair, we can ignore the color and add (red die) + (blue die), giving 11 possible sums, each of which possibly occurring in a multiplicity of ways:
Sum No. of ways Probability
--- ----------- -----------
2 1 1/36 \
3 2 2/36 \
4 3 3/36 \
5 4 4/36 \
6 5 5/36 \ probability
7 6 6/36 > distribution
8 5 5/36 /
9 4 4/36 /
10 3 3/36 /
11 2 2/36 /
12 1 1/36 /
----- ----
total 36 36/36 = 1
