A and B roll a pair of dice in turn, with A rolling first. A’s objective is to obtain a sum of 6, and B’s is to obtain a sum of 7. The game ends when either player reaches his or her objective, and that player is declared the winner.

(a) Find the probability that A is the winner.

(b) Find the expected number of rolls of the dice.

(c) Find the variance of the number of rolls of the dice.