Craps is a gambling game in which the players make a wager on the outcome of a roll of a a pair of dice. The basic rules of the game, whether it be played in a casino or on the street, are quite simple. Each player (called a shooter) gets turns rolling two dice, and calculating the value of the roll as the sum of the face values. Each turn has two phases: "come out" and "point". In order to enter the game the shooter has to make a "come out" roll. A come out roll of value 2, 3, or 12 is called "craps" or "crapping out", and the shooter loses the initial wager she made. A come out roll of 7 or 11 is called a "natural" and the shooter wins the bet automatically. If the roll lands on any other possible number, i.e. 4, 5, 6, 8, 9, 10 it establishes that value as the "point". Once a point has been established, the shooter must roll the same point value again in order to win. If she rolls a 7 before she rolls her point, she is said to have "sevened out", and loses the bet. Keeping in mind that the game involves rolling a pair of dice, answer the following questions.

(i) How many events constitute the sample space of a roll of a pair of dice

(ii) What is the probability that a shooter will "crap out" on the come out roll

(iii) What is the probability that the shooter rolls a "natural"

(iv) What is, then, the probability of establishing a "point"? (Hint: Remind yourself of the very basic rules of probability we discussed and save yourself the trouble of doing too many calculations!)