# Question

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

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.

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.

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