1) Die A has orange on one face and blue on five faces. Die C has orange on three faces and blue on three faces. All are unbiased dice. If the three dice are rolled, find the probability that exactly two of the three dice come up orange.
2) Suppose that A, B, and C are mutually independent events and that P(A) = 0.5, P(B) =0.8, and P(C) = 0.9. Find the probabilities that a) all three events occur, b) exactly two of the three events occur, and c) none of the events occur.
The solution contains the determination of various probabilities of compound events.