When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 5.1 on page 206. 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.