Question

According to the National Automobile Dealers Assoc., 75% of U.S. car dealers' profits comes from
repairs and parts sold. However, many of the dealerships' service departments aren't open evenings
or weekends. The percentage of dealerships opened during the evenings and weekends are as
follows:
Time Dealerships are Open					Percentage of Dealerships
Weekends but not evenings						37.5
Evenings but not weekends						13.2
Both evenings and weekends						11.3
a. Are the listed times mutually exclusive?
b. What is the probability that a car dealership selected at random is not open in the
evenings or on the weekends?
c. Suppose two car dealerships, say, Dealership A and Dealership B, are each selected at
random from car dealerships in the United States. What is the probability that both are open
in the evenings but not on the weekends, or that both are open on the weekends but not in
the evenings?
d. For the two dealerships in part c, what is the probability that Dealership A is open in the
evenings but not on the weekends, and Dealership B is open on the weekends but not in the
evenings?
e. For the two dealerships in part c, what is the probability that one of them is open in the
evenings but not on the weekends, and that the other is open on the weekends but not in the
evenings?

Answer 1