An urn initially contains one red and one blue ball. At each stage, a ball is randomly chosen and then replaced along with another of the same color. Let X denote the selection number of the first chosen ball that is blue. For instance, if the first selection is red and the second blue, then X is equal to 2.
(a) Find P{X > i},i ≥ 1.
(b) Show that with probability 1, a blue ball is eventually chosen. (That is, show that P{X<∞} = 1.)
(c) Find E[X].
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