Concept explainers
Nontransitive Dice Consider three dice: one red, one blue, and one green. The sides of the red die contain the numbers 3 3 3 3 3 6, the sides of the blue die contain the numbers 2 2 2 5 5 5, and the sides of the green die contain the numbers 1 4 4 4 4 4.
(a) Determine the probability that the red die will show a higher number than the blue die when both are tossed.
(b) Determine the probability that the blue die will show a higher number than the green die when both are tossed.
(c) Determine the probability that the green die will show a higher number than the red die when both are tossed.
(d) What is surprising about the results in parts (a)–(c)?
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Finite Mathematics & Its Applications (12th Edition)
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