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