Three faces of a die are black, two faces are white and one face is red. The die is tossed three times. What is the probability that the colours black, white and red appear in the first, second and third tosses respectively?

Step-by-step solution

Total number of faces on the die is 6 . Number of black faces is 3 . Probability of getting a black face in the first toss is P(B) = 3 6 = 1 2 . Number of white faces is 2 . Probability of getting a white face in the second toss is P(W) = 2 6 = 1 3 . Number of red faces is 1 . Probability of getting a red face in the third toss is P(R) = 1 6 . Since the tosses are independent events, the required probability is the product of the individual probabilities. Required probability = P(B) P(W) P(R) = 1 2 1 3 1 6 = 1 36 .