Solve the following:
Q: A popular dice game, called "craps," is played in the following manner. A player starts by rolling two dice. If the result is a 7 or 11, the player wins. If the result is 2, 3, or 12, the player loses. For any other sum appearing on the dice, the player continues to roll the dice until that outcome reoccurs (in which case the player wins) or until a 7 occurs (in which case the player loses).
a) What is the probability that a player wins the game on the first roll of the dice?
b) What is the probability that a player loses the game on the first roll of the dice?
c) If the player throws a 4 on the first roll, what is the probability that the game ends on the next roll?
d) If the player throws a 4 on the first roll, what is the probability that he will eventually win the game?