Anna and Steve play the following game. A die is thrown until either a five or a six appears for the first time. If the number of throws X is even, then Anna gives Steve the amount of a dollars; if X is odd, Anna receives from Steve b dollars.

(i) What is the probability function of X?

(ii) What is the probability that Anna wins this game?

(iii) Show that for the game to be fair, we must have 2a = 3b.