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Car owners are required to have car insurance to ensure that any damage they cause to themselves or other drivers can be repaired. Suppose that there are three car insurance companies A, B and C to choose from. Each of these insurance companies sells annual policies, so it is only possible to change insurer once a year. Moreover, new customers are required to stay with their insurer for a minimum of two years. When it is possible for a car owner to change their insurance company, the probability that they will not choose to do so is 0.8, 0.7 and 0.9 if the current insurer is company A, B or C respectively. If, when it is possible for a car owner to change their insurance company, they choose to do so, then the probability of selecting either of the alternate firms is 0.5. A driver has just changed his car insurance to company A. Given that the driver will change their insurer again at some point in the future, calculate the expected time until the driver makes the change.

Car owners are required to have car insurance to ensure that any damage they cause to themselves or other drivers can be repaired. Suppose that there are three car insurance companies A, B and C to choose from. Each of these insurance companies sells annual policies, so it is only possible to change insurer once a year. Moreover, new customers are required to stay with their insurer for a minimum of two years. When it is possible for a car owner to change their insurance company, the probability that they will not choose to do so is 0.8, 0.7 and 0.9 if the current insurer is company A, B or C respectively. If, when it is possible for a car owner to change their insurance company, they choose to do so, then the probability of selecting either of the alternate firms is 0.5. A driver has just changed his car insurance to company A. Given that the driver will change their insurer again at some point in the future, calculate the expected time until the driver makes the change.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Car owners are required to have car insurance to ensure that any damage they cause to themselves or other drivers can be repaired. Suppose that there are three car insurance companies A, B and C to choose from. Each of these insurance companies sells annual policies, so it is only possible to change insurer once a year. Moreover, new customers are required to stay with their insurer for a minimum of two years. When it is possible for a car owner to change their insurance company, the probability that they will not choose to do so is 0.8, 0.7 and 0.9 if the current insurer is company A, B or C respectively. If, when it is possible for a car owner to change their insurance company, they choose to do so, then the probability of selecting either of the alternate firms is 0.5. A driver has just changed his car insurance to company A. Given that the driver will change their insurer again at some point in the future, calculate the expected time until the driver makes the change.
Transcribed Image Text:Car owners are required to have car insurance to ensure that any damage they cause to themselves or other drivers can be repaired. Suppose that there are three car insurance companies A, B and C to choose from. Each of these insurance companies sells annual policies, so it is only possible to change insurer once a year. Moreover, new customers are required to stay with their insurer for a minimum of two years. When it is possible for a car owner to change their insurance company, the probability that they will not choose to do so is 0.8, 0.7 and 0.9 if the current insurer is company A, B or C respectively. If, when it is possible for a car owner to change their insurance company, they choose to do so, then the probability of selecting either of the alternate firms is 0.5. A driver has just changed his car insurance to company A. Given that the driver will change their insurer again at some point in the future, calculate the expected time until the driver makes the change.
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