An urn has 8 red and 12 blue balls. Suppose that balls are chosen at random and

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An urn has 8 red and 12 blue balls. Suppose that balls are chosen at random and removed from the urn, with the process stopping when all the red balls have been removed. Let X be the number of balls that have been removed when the process stops.

(a) Find P(X = 14).

(b) Find the probability that a specified blue ball remains in the urn.

(c) Find E[X].

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