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Suppose that A1,...,Ak form a sequence of k independent

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Suppose that A1,...,Ak form a sequence of k independent events. Let B1,...,Bk be another sequence of k events such that

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Suppose that A1,...,Ak form a sequence of k independent events. Let B1,...,Bk be another sequence of k events such that for each value of j (j = 1, . . . , k), either Bj = Aj or Bj = Ac j . Prove that B1,...,Bk are also independent events. Hint: Use an induction argument based on the number of events Bj for which Bj = Ac j .

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