Question: Problem 2.72 Suppose A, B, C are mutually independent events. Assume that P(B C) > 0this hypothesis is just to ensure that the conditional

Problem 2.72 Suppose A, B, C are mutually independent events. Assume that P(B ∩ C) > 0—this hypothesis is just to ensure that the conditional probabilities below are defined.

(a) Show that P(A|B ∩ C) = P(A).

(b) Show that P(A|B ∪ C) = P(A).

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