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There are risky drivers and safe drivers. The number of accidents that a risky driver will...

There are risky drivers and safe drivers. The number of accidents that a risky driver will have in a year is Poisson with expected value of 2. The number of accidents that a safe driver will have in a year is also Poisson, but with an expected value of 1. Suppose that 1⁄4 of the population are risky drivers and the remainder are safe drivers.

A. A person is selected at random and found to have 2 accidents this year. What is the probability that this driver is a risky driver?

B. Assume that the loss from each accident is $2500. How much should the insurance company price the policy of the driver in A. in the next year so that the company makes $500 more than the expected loss?

C. To be risk averse, the insurance company has 100 policies of people they assume are all risky drivers (i.e., each has a Poisson number of accidents with mean of 2 and are independent). If they charge each of these customers $6,000, what is the approximate probability that the total loss from these 100 policies, assuming that they are all risky drivers, exceed the amount that the insurance company charges?

Math   Statistics-And-Probability   
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