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  3. suppose that nn independent trials are performed,

Suppose that nn independent trials are performed, with trial ii being a success with probability 1/(2i+1).12i1....

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Basic Math

Suppose that nn independent trials are performed, with trial iibeing a success with probability 1/(2i+1).12i1. Let PnPndenote theprobability that the total number of successes that result is anodd number.

1.Find Pn for n=1,2,3,4,5.

2.Conjecture a general formula for Pn.

3. Derive a formula for Pn in terms of Pn−1

Verify that your conjecture in part (b) satisfies the recursiveformula in part (c). Because the recursive formula has a uniquesolution, this then proves that your conjecture is correct.

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