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
E)None of the above

Question

Quizplus · Accepted Answer

Let A = event that customer uses pick-up and delivery service
Let B = event that customer opens an account
P(A) = 0.6 (given)
P(B) = 0.6 (given)
P(A∩B) = P(B|A)P(A) = 0.6*0.6 = 0.36 (using multiplication rule)
Now, we need to find the probability that a customer uses only one of these services, which can be represented as (A∩B')∪(A'∩B), which means the event that a customer uses pick-up and delivery service but does not open an account or the event that a customer opens an account but does not use the pick-up and delivery service.
Using the formula for union of two events: 
P((A∩B')∪(A'∩B))= P(A∩B')+P(A'∩B)

We know that P(A∩B') = P(A) - P(A∩B) (using subtraction rule)
P(A∩B') = 0.6 - 0.36 = 0.24

Also, P(A'∩B) = P(B) - P(A∩B) (using subtraction rule)
P(A'∩B) = 0.6 - 0.36 = 0.24

Therefore, P((A∩B')∪(A'∩B))= P(A∩B')+P(A'∩B) = 0.24 + 0.24 = 0.48

Hence, the probability that a customer uses only one of these services is 0.48. Therefore, the correct answer is (C) 0.48.

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