For this problem, use the fact that the expected value of an event is a probability weighted average, the sum of each probable outcome multiplied by the probability of the event occurring.

You own a house worth $800,000 that is located on a river. If the river floods moderately, the house will be completely destroyed. This happens about once every 50 years. If you build a seawall, the river would have to flood heavily to destroy your house, which only happens about once every 100 years. What would be the annual premium without a seawall for an insurance policy that offers full insurance?

Without a seawall, the annual premium is?

(Round your response to the nearest whole number.)

What would be the annual premium with a seawall for an insurance policy that offers full insurance?

With a seawall, the annual premium is?

(Round your response to the nearest whole number.)

For a policy that only pays 75% of the home value, what are your expected costs without a seawall?

Without a seawall, the expected cost is?

(Round your response to the nearest whole number.)

For a policy that only pays 75% of the home value, what are your expected costs with a seawall?

With a seawall, the expected cost is?

(Round your response to the nearest whole number.)

Do the different policies provide an incentive to be safer (i.e., to build the seawall)?