A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge.Management believes 60 percent of the existing customers will take advantage of this service.They are also considering offering customers the option of opening an account and receiving monthly bills.They believe 60 percent of customers (regardless of whether or not they use the pick-up service)will use the account service.If the two services are introduced to the market, what is the probability that a customer uses only one of these services?
A)0.40
B)0.60
C)0.48
D)0.24

Question

Quizplus · Accepted Answer

Let P(P) denote the probability that a customer uses the pick-up service
Let P(A) denote the probability that a customer uses the account service

P(P) = 0.6 (given)
P(A) = 0.6 (given)

Let P(P and A) denote the probability that a customer uses both services
P(P and A) = P(P) * P(A) = 0.6 * 0.6 = 0.36

Now, we need to find the probability that a customer uses only one of these services. This can happen in two ways:

1) A customer uses only the pick-up service, not the account service.
In this case, the probability is P(P) - P(P and A) = 0.6 - 0.36 = 0.24

2) A customer uses only the account service, not the pick-up service.
In this case, the probability is P(A) - P(P and A) = 0.6 - 0.36 = 0.24

Adding these probabilities, we get:
P(using only one service) = 0.24 + 0.24 = 0.48

Therefore, the best choice is C) 0.48.

A Dry Cleaning Business Offers a Pick-Up and Delivery Service