In a certain board game participants roll a standard six-sided die and need to hit a particular value to get to the finish line exactly. For example, if Carol is three spots from the finish, only a roll of 3 will let her win; anything else and she must wait another turn to roll again. The chance of getting the number she wants on any roll is p = 1/6 and the rolls are independent of each other. We let a random variable X count the number of turns until a player gets the number needed to win. The possible values of X are 1, 2, 3, . . . and the probability function for any particular count is given by the formula

(a) Find the probability a player finishes on the third turn.
(b) Find the probability a player takes more than three turns to finish.

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P(X = k) = p(1 – p)k-1