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In his autobiography A Sort of Life, British author Graham Greene described a period of severe mental depression during which he played Russian Roulette. This â€œgameâ€™s consists of putting a bullet in one of the six chambers of a pistol, spinning the chambers to select one at random, and then firing the pistol once at oneâ€™s head.

a. Greene played this game six times and was lucky that none of them resulted in a bullet firing. Find the probability of this outcome.

b. Suppose that he had kept playing this game until the bullet fired. Let Y denote the number of the game on which it fires. Show the probability mass function for Y, and justify.

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