# Question: An urn initially contains one red and one blue ball

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].

(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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