In his autobiography A Sort of Life, British author Graham Greene described a period of severe mental depression during which he played Russian Roulette — 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 one’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 he had kept playing this game until the bullet fires. Let Y denote the number of the game on which the bullet fires. Explain why the probability of the outcome y equals (5/6)y−1(1/6), for y = 1, 2, 3,... . (This is called the geometric distribution.)