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A sequence of n ≥1 independent trials is performed, where each trial ends in "success" or "failure" (but not both). Let pi be the probability of success in the ith trial, qi=1-pi, and bi=qi-1 / 2, for i=1,2, …, n. Let An be the event that the number of successful trials is even. (a) Show that for n=2, P(A2)=1 / 2 2 b1 b2. (b) Show by induction that P(An)=1 / 2 2^n-1 b1 b2 …bn (This result is very useful in cryptography. Also, note that it implies that if n coins are flipped, then the probability
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