Dice. When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 4.1 on page 181. Let Y denote the sum of the dice.

a. What are the possible values of the random variable Y ?

b. Use random-variable notation to represent the event that the sum of the dice is 7.

c. Find P(Y = 7).

d. Find the probability distribution of Y . Leave your probabilities in fraction form.

e. Construct a probability histogram for Y .

In the game of craps, a first roll of a sum of 7 or 11 wins, whereas a first roll of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is rolled. Determine the probability of

f. a win on the first roll.

g. a loss on the first roll.