A black and a red die are rolled together. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.

S = {(1,1), (1,2), .....(6,6)}

∴ n(S) = 36

A = Red die resulted in a number less than 4.

= { (1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3), (4,1), (4,2), (4,3), (5,1), (5,2), (5,3), (6,1), (6,2), (6,3)}

n(A) = = 18

B = sum of number is 8

B = {(4,4), (6,2), (2,6), (5,3), (3,5)}

n(B) = = 5

AB = {(5,3), (6,2)}

n(A B) = = 2

∴ P() = Probability of sum of numbers 8 when Red die resulted in a number less than 4

= .