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A jar contains 8 black and 2 red marbles. Marbles are drawn with re- placement until a red one is found. (a) Write down an

A jar contains 8 black and 2 red marbles. Marbles are drawn with re-

placement until a red one is found.

(a) Write down an expression representing the probability that it will

take k drawings.

(b) How many drawings would you expect to make?

In the setup of the previous problem, if 3 marbles are drawn without

replacement, what is the expected number of red marbles removed?

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