A pair of dice is rolled and the sum of the number is noted

A pair of dice is rolled and the sum of the number is noted. what is the probability that the sum of 8 does not occur?

Solution

The required probability is -

1 - p(sum of 8 occurs)

S (sample space) = (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)

E (sum of 8 occurs) = (2,6), (6,2), (3,5), (5,3), (4,4)

p (sum of 8 occurs) = n(E) / n(S) = 5/36

p(sum of 8 does not occur) = 1 - (5/36) = 31/36