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# Expected value of an insurance policy

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1. You own a \$9,000 car and a \$850 mountain bike. The probability that your car will be stolen next year is 0.02, but the probability that your bike will be snatched is 0.1. An insurance company offers you theft insurance for your car for \$200 and the insurance for your bike for \$75.
a) Compute the expected value of the car and bike insurance policy to the insurance company.
b) As an insurance policy holder, do you get a "good deal" from this car and bike insurance? Explain your response.

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##### Solution Summary

This post answers how to calculate the expected value of an insurance policy to the insurance company and discuss whether the deal is good for the insuree.

##### Solution Preview

Question 1:

Car Insurance
Cost of car = \$9,000
Probability of loss due to theft = 0.02
Expected cost of loss = 0.02*9000=\$180
Premium on car insurance = \$200
Expected value of car insurance policy to the insurance company = \$200-\$180=\$20.00 per policy

Bike Insurance
Cost of bike = \$8,50
Probability of loss ...

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