Question

Two dice rolled. What is the probability of obtaining a sum greater than 9, but less than 13?

Answer 1

Two dice rolled, hence sample space is -

S = { (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) }

n(S) = 36

Let, A be the event that sum is greater than 9 but less than 13.

So, A = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}

n(A) = 6

Probability that sum is greater than 9 but less than 13 is -

..... (By defintion of probability)

Hence, Probability that sum is greater than 9 but less than 13 is 0.1666.