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 “game” 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 one’s head.

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

b. Suppose one kept playing this game until the bullet fires. Let Y denote the number of the game on which the bullet fires. Argue that the probability of the outcome y equals (5/6)y−1(1/6), for y = 1, 2, 3, . . . . (This is called the geometric distribution.)