Suppose you roll three distinguishable fair dice and call the resulting numbers a, b, and c Dene events X a b is even, Y b c is even, and Z a c is even Prove that these three events are pairwise independent but not mutually independent ...

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Suppose you roll three distinguishable fair dice and call the resulting numbers a, b, and c. Dene

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Question:

Suppose you roll three distinguishable fair dice and call the resulting numbers a, b, and c. Deﬁne events X = “a + b is even,” Y = “b + c is even,” and Z = “a + c is even.” Prove that these three events are pairwise independent but not mutually independent.