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A dry-cleaning business offers a pick-up and delivery service for a 15 percent surcharge. Management believes 70 percent of existing customers will use this service. They are also considering offering customers the option of opening an account and receiving monthly bills, which they believe 40 percent of customers will use, independent of whether they use the pick-up service.

If both services are introduced to the market, what is the probability that a customer uses only one of these services, but not the other?

Please show your work.

Answer :

Final answer:

The probability that a customer uses only one of these services, but not the other, is 30%.

Explanation:

To find the probability that a customer uses only one of these services, but not the other, we can use conditional probability. Let's denote the event of using the pick-up and delivery service as A, and the event of using the account service as B.

From the given information, we know that 70% of the existing customers will take advantage of the pick-up and delivery service, and 40% of customers will use the account service.

Using conditional probability, we can calculate the probability of using only one service:

  1. Probability of using only the pick-up and delivery service (A but not B): P(A and not B) = P(A) - P(A and B)
  2. Probability of using only the account service (B but not A): P(B and not A) = P(B) - P(A and B)

Substituting the given probabilities, we have:

  • P(A and not B) = 0.70 - 0.40 = 0.30
  • P(B and not A) = 0.40 - 0.40 = 0.00

Since the probability of using only the account service (B but not A) is 0.00, it means that no customer will use only the account service without using the pick-up and delivery service. Therefore, the probability that a customer uses only one of these services, but not the other, is 0.30 or 30%.

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