Question

Известно, что оператор сервисного центра может самостоятельно решить проблему клиента с вероятностью 0,7. В противном случае он передает звонок в службу технической поддержки, где дежурный может решить проблему по телефону с вероятностью 0,6. В сложном случае инженер выезжает на дом к клиенту, где проблема решается с вероятностью 0,9. Какова вероятность того, что после звонка клиента неисправность устранена на дому?

Answer 1

Problem Statement

A service center operator has a 0.7 probability of independently resolving a customer's problem. Otherwise, the call is transferred to the technical support department, where the on-duty technician has a 0.6 probability of resolving the problem over the phone. In complex cases, an engineer visits the customer's home, where the problem is resolved with a 0.9 probability. What is the probability that the problem is resolved at the customer's home after the customer's call?

Solution

To find the probability that the problem is resolved at the customer's home after the customer's call, we need to consider the different scenarios that can occur.

1. The service center operator resolves the problem independently with a probability of 0.7. 2. The service center operator transfers the call to the technical support department, where the on-duty technician resolves the problem over the phone with a probability of 0.6. 3. The service center operator transfers the call to the technical support department, and the problem is not resolved over the phone. In this case, an engineer visits the customer's home, and the problem is resolved with a probability of 0.9.

We can calculate the probability of each scenario and then combine them to find the overall probability.

Let's calculate the probabilities:

1. Probability that the service center operator resolves the problem independently: 0.7. 2. Probability that the service center operator transfers the call to the technical support department and the on-duty technician resolves the problem over the phone: (1 - 0.7) * 0.6 = 0.3 * 0.6 = 0.18. 3. Probability that the service center operator transfers the call to the technical support department, the problem is not resolved over the phone, and an engineer visits the customer's home to resolve the problem: (1 - 0.7) * (1 - 0.6) * 0.9 = 0.3 * 0.4 * 0.9 = 0.108.

To find the overall probability that the problem is resolved at the customer's home after the customer's call, we add the probabilities of scenarios 2 and 3:

0.18 + 0.108 = 0.288.

Therefore, the probability that the problem is resolved at the customer's home after the customer's call is 0.288.