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Accident records collected by an automobile insurance
Chapter 3, Problem 206SE(choose chapter or problem)
Problem 206E
Accident records collected by an automobile insurance company give the following information. The probability that an insured driver has an automobile accident is .15. If an accident has occurred, the damage to the vehicle amounts to 20% of its market value with a probability of .80, to 60% of its market value with a probability of .12, and to a total loss with a probability of .08. What premium should the company charge on a $12,000 car so that the expected gain by the company is zero?
Questions & Answers
QUESTION:
Problem 206E
Accident records collected by an automobile insurance company give the following information. The probability that an insured driver has an automobile accident is .15. If an accident has occurred, the damage to the vehicle amounts to 20% of its market value with a probability of .80, to 60% of its market value with a probability of .12, and to a total loss with a probability of .08. What premium should the company charge on a $12,000 car so that the expected gain by the company is zero?
ANSWER:
Answer:
Step 1 of 1:
The probability that an insured driver has an accident is
If an accident has occurred, the damage to the vehicle amounts to of its price with a probability of to 60% of its price with a probability of and to a total loss with a probability of
What premium should the company charge on a car price so that the expected gain by the company is zero?
Let represent the gain to the insurance company for a particular insured driver.
Let be the premium charged to the car driver.
Using above information, we can form the probability distribution for