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.

Let E be the event of getting a sum of 8 on both the dice.
F be the event that the red die resulted in a number less than 4.

E: (2,6), (3,5), (4,4), (5,3), (6,2)
P(E) = 5/36

F: (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)
P(F) = 18/36 = 1/2

P(E∩F) = 2/36

Now, P(E/F) = P(E∩F) / P(F) = (2/36) / (1/2) = 1/9