Suppose that n independent trials are performed, with trial i being a success with probability 1/(2i + 1). Let Pndenote the probability that the total number of successes that result is an odd number.
(a) Find Pnfor n =1, 2, 3, 4, 5.
(b) Conjecture a general formula for Pn.
(c) Derive a formula for Pnin terms of Pn−1
(d) Verify that your conjecture in part (b) satisfies the recursive formula in part (c). Because the recursive formula has a unique solution, this then proves that your conjecture is correct.
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