Two number cubes are rolled. What is the probability that the sum of the numbers rolled is either a 6 or an 8?

Let us assume that the cubes are numbered from 1 to 6 in their six faces.

When these two cubes are rolled, the possible values could be,

(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)

Total possibilities are 36.

Now the sum of the numbers are either 4 or 10. Those numbers are

(1,3) (2,2) (3,1) - > this sums to 6

(4,6) (5,5) (6,4) - > this sums to 8

Total possibilities of getting sum 4 or 10 is 6.

So, the possibility of getting sum of or from a pair of rolled cubes is

6/36 = 1/6