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Let A1, A2,... be an arbitrary infinite sequence of even

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Let A1, A2,... be an arbitrary infinite sequence of events, and let B1, B2,... be another infinite sequence of events de

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Let A1, A2,... be an arbitrary infinite sequence of events, and let B1, B2,... be another infinite sequence of events defined as follows: B1 = A1, B2 = Ac 1 ? A2, B3 = Ac 1 ? Ac 2 ? A3, B4 = Ac 1 ? Ac 2 ? Ac 3 ? A4,.... Prove that Pr n i=1 Ai =n i=1 Pr(Bi) for n = 1, 2,..., and that Pr ? i=1 Ai =? i=1 Pr(Bi).

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