# What is the probability that a player wins the game on the first roll of dice?

A favorite casino game of dice “craps” is played in the following manner: A player starts by rolling a pair of balanced dice. If the roll (the sum of two numbers showing on the dice) results in a 7 or 11, the player wins. If the roll results in a 2 or 3 (called “craps”) the player loses. For any other roll outcome, the player continues to throw the dice until the original roll outcome recurs (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 dice?

b. What is the probability that a player loses the game on the first roll of dice?

c. If the player throws a total of 4 on the first roll, what is the probability that the player wins in the next roll?

d. If the player throws a total of 4 on the first roll, what is the probability that the player loses in the next roll?

e. If the player throws a total of 4 on the first roll, what is the probability that the game ends in the next roll? (win or lose)

f. If the player throws a total of 4 on the first roll, what is the probability that the game continues after the next roll?