Two fair sixsided dice are rolled What is the probability of

Two fair six-sided dice are rolled. What is the probability of observing a sum on the faces that is greater than 9?

Solution

Total number of outcomes = 6*6 = 36

For sum greater than 9 :

Sum = 10 : (4,6);(6,4);(5,5)
Sum = 11 : (5,6);(6,5)
Sum = 12 : (6,6)

Total possible cases = 3 +2 +1 = 6

P(Sum > 9) = 6/36 = 1/6 = 0.1667 Answer