Question

A pair of the die is rolled once. What is the probability that the sum of the value' on the two die  faces is not a 7?

Answer 1

When two dice are rolled once, we have 36 possibilities as shown below
(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)

We need to find P(Sum of two values of two dices is not 7)

P(Sum of two values of two dices is not 7) = 1 - P(Sum of two values of two dices equals to  7)

for "Sum of two values of two dices equals to 7", we have 6 cases as shown below (1,6)  (2,5) (3,4)  (4,3)  (5,2)  (6,1)

=> P(Sum of two values of two dices equals to  7) = 6/36 = 1/6

P(Sum of two values of two dices is not 7) = 1 - P(Sum of two values of two dices equals to  7)

= 1- 1/6 = 5/6

So, the answer is 5/6