A dry cleaning business offers a pick-up and delivery service for a 10 percent surcharge.Management believes 60 percent of 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 their 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 a customer uses both services?
A)0.12
B)0.60
C)0.36
D)0.24

Question

Quizplus · Accepted Answer

Let A be the event that a customer uses the pick-up and delivery service and B be the event that a customer opens an account.

We are given:
P(A) = 0.6 (60% of customers will use the pick-up service)
P(B) = 0.6 (60% of customers will open an account)
P(A|B) = P(A intersect B)/P(B)

We need to find P(A intersect B), the probability that a customer uses both services.

To do this, we can use the formula:
P(A intersect B) = P(B) * P(A|B) 
P(A intersect B) = 0.6 * P(A|B)

We don't have enough information to find P(A|B) directly, but we can use the fact that 10% of customers will be charged a surcharge for the pick-up service. This means that if a customer opens an account, they will also be charged the surcharge if they use the pick-up service.

So, if B occurs (a customer opens an account), then the probability that a customer will use the pick-up service and be charged the surcharge is: 
P(A|B) = 0.6 + 0.4*0.1 = 0.64

Now we can find: 
P(A intersect B) = 0.6 * 0.64 = 0.384

Therefore, the probability that a customer uses both services is 0.384 or 38.4%, which is closest to 0.36 (choice C).

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