Let D1, D2, D3 be three four-sided dice whose sides have been labeled as follows: D1

QUESTION:

Let D1, D2, D3 be three four-sided dice whose sides have been labeled as follows: D1 : 0333 D2 : 2225 D3 : 1146 The three dice are rolled at random. Let A, B, and C be the events that the outcome on die D1 is larger than the outcome on D2, the outcome on D2 is larger than the outcome on D3, and the outcome on D3 is larger than the outcome on D1, respectively. Show that (a) P(A) = 9/16, (b) P(B) = 9/16, and (c) P(C) = 10/16. Do you find it interesting that each of the probabilities that D1 beats D2, D2 beats D3, and D3 beats D1 is greater than 1/2? Thus, it is difficult to determine the best die.