Chapter 13.1, Problem 65E

The casino game of craps is played by a person called the shooter, who rolls two dice. There are two phases to the game. The first phase is called the “come out” phase, and the second is called the “point” phase. Exercises 65 and 66 investigate the probabilities involved with playing craps.

Playing craps. A come-out roll of $2,3,\text{ or }12$ is called “craps” or “crapping out,” and the shooter loses. If the “come out” roll is a 7 or 11, the shooter wins. Otherwise, the game progresses to the “point” phase. If the shooter rolls the pair of dice,

a. what is the probability that the player craps out?

b. what is the probability that the player wins?

c. what is the probability that the player progresses to the point phase?