Question: Problem 5.12 Non-transitive dice: Consider 3 six-sided dice whose faces are labeled as follows: Die 1 = {5, 7, 8, 9, 10, 18}; Die 2

Problem 5.12 Non-transitive dice: Consider 3 six-sided dice whose faces are labeled as follows: Die 1 = {5, 7, 8, 9, 10, 18}; Die 2 = {2, 3, 4, 15, 16, 17}; Die 3 = {1, 6, 11, 12, 13, 14}. Let Yi denote the number that turns up when the ith die is rolled. Assume that the three random variables Y1, Y2, Y3 are mutually independent. Show that P(Y1 > Y2) = P(Y2 > Y3) = P(Y3 > Y1) = 21/36.

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