Question

*There are numerous similar questions to this on here but I'm almost positive that they're incorrect so please someone answer this question differently and correctly. Thank you

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 35.4

Evenings but not weekends 13.8

Both evenings and weekends 11.1

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

Let W be the event that dealerships opened during the weekend

then the probability that the dealerships will be open during the weekend is

E be the event that dealerships opened during the evening

then the probability that the dealerships will be open during the evening is

the probability that the dealerships will be open during the evening and weekend is

a)  two events are mutually exclusive or disjoint if they cannot both occur at the same time

here

hence these events are not mutually exclusive.

b)  the probability that a car dealership selected at random is not open in the evenings or on the weekends =

C) The probability that one dealership opens in the evening(or say weekend) is independent of the other dealership.

The probability that Dealership A opens in the evening is the same as that of dealership B. P(E) = 0.138

same goes for weekends P(W ) = 0.354

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) 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) 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 =