Question

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. 

Answer 1

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