The game of 'Chuck-a-Luck' is played as follows. Three fair dice are rolled. You, as the bettor, place a $1 bet on the occurrence of one of the integers 1, 2, 3, 4, 5 or 6. Suppose you bet on the occurrence of a 5. If at least one 5 occurs on the three dice, you win back your stake of $1 and in addition $1 for each 5 that occurs, unless all three die show a 5, when you win $5 along with your stake. If no 5s occur then you lose your stake of $1. (The same rules apply to any of the 6 numbers.) Let V be the net amount you win in one play of this game (loss = negative gain).

(a) Find the probability function of V .

(b) Calculate E(V ), and state whether the game is fair