(a) What is the probability of an even number of successes
Chapter , Problem 32(choose chapter or problem)
(a) What is the probability of an even number of successes in n independent Bernoulli trials? Hint: Let rn be the probability of an even number of successes in n Bernoulli trials. By conditioning on the first trial and using the law of total probability (Theorem 3.3), show that for n 1, rn = p(1 rn1) + (1 p)rn1. Then prove that rn = 1 2 4 1 + (1 2p)n5 . (b) Prove that [ . n/2] k=0 ; n 2k < p2k (1 p)n2k = 1 2 4 1 + (1 2p)n5 .
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