In the game of craps, a player rolls two balanced dice. Thirty-six equally likely outcomes are possible, as shown in Fig. 5.1 on page 187. Let
A = event the sum of the dice is 7,
B = event the sum of the dice is 11,
C = event the sum of the dice is 2,
D = event the sum of the dice is 3,
E = event the sum of the dice is 12,
F = event the sum of the dice is 8, and
G = event doubles are rolled.
a. Compute the probability of each of the seven events.
b. The player wins on the first roll if the sum of the dice is 7 or 11. Find the probability of that event by using the special addition rule and your answers from part (a).
c. The player loses on the first roll if the sum of the dice is 2, 3, or 12. Determine the probability of that event by using the special addition rule and your answers from part (a).
d. Compute the probability that either the sum of the dice is 8 or doubles are rolled, without using the general addition rule.
e. Compute the probability that either the sum of the dice is 8 or doubles are rolled by using the general addition rule, and compare your answer to the one you obtained in part (d).