Elizabeth has two identical number cubes. both cubes have faces numbered 1 through 6. If Elizabeth rolls each cube once, What is the probability that the sum of the two numbers on the top faces will be 10.

The sample space for the two identical dice (outcomes):

(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 if Elizabeth rolls each cube once, there is 36 (6 x 6) possible outcomes.

Let E = event of getting a sum of 10.

The number which is a sum 10 will be:

E = [ (4,6), (5,5), (6,4) ]

P (E) = number of favorable outcomes divided by total number of possible outcomes

= 3 / 36 or 0.083