13. A game of craps is played with a pair of fair dice as follows. A player rolls the dice.

If a sum of 7 or 11 shows up, the player wins; if a sum of 2, 3, or 12 shows up, the player loses. Otherwise the player continues to roll the pair of dice until the sum is either 7 or the first number rolled. In the former case the player loses and in the latter the player wins.

(a) Find the probability that the player wins on the nth roll.

(b) Find the probability that the player wins the game.

(c) What is the probability that the game ends on: (i) the first roll, (ii) second roll, and (iii) third roll?