You roll two six-sided fair number cubes. What is the probability that you will roll a sum greater than 6?

Total possible outcomes = 6 x 6 = 36

Listed here are all the possible 36 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)

Total outcomes that have a sum greater than 6 = 21

Listed here are the possible outcome greater than 6:

(1,6) (2,5) (2,6) (3,4) (3,5) (3,6) (4,3) (4,4) (4,5) (4,6) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

P (sum greater than 6) = 21/36 = 7/12

Answer: P (sum greater than 6) = 7/12