Question

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 ?$800, 000 that is located on a river. If the river floods? moderately, the house will be completely destroyed. This happens about once every 20 years. If you build a? seawall, the river would have to flood heavily to destroy your? house, which only happens about once every 200 years. What would be the annual premium without a seawall for an insurance policy that offers full? insurance? Without a? seawall, the annual premium is ?$ 40000. ?(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 ?$ 4000. ?(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 ?$ nothing. ?(Round your response to the nearest whole? number.)

Answer 1

Solution

Step (1)

Refer to the following table that lists the expected values of the house that remains W flood with and without a seawall:

Step (2)

The expected values are calculated by multiplying the chances of each event occurring (heavy or moderate flooding) by the value of the house if that respective event were to take place. Take the cell in red for example. The chances of a moderate flood occurring are 0.02. When this happens and there is no seawall built, the value of the house is reduced to $0 because it will be completely destroyed. The remaining 0.98 probability indicates the changes of a moderate flood not occurring, during which the house will retain its full value of $800,000 because it remains standing. Therefore, the expected value of the house is $784,000 when there is a moderate flood and no seawall is built.

Step (3)

Refer to the cells in blue. When there is a heavy flood, the value of the house will be reduced to SO regardless if there is a seawall built because the wall cannot withstand the flood. That is why there is a 100% (or 1.00) chance that the house's value will drop to $0. Conversely, there is a 0% chance that the house will retain its value of $800,000 when a heavy flood occurs.

Step (4)

Refer to the cell green. When there is a moderate flood, the value of the house will remain at $800,000 when there is a seawall built because it protects against the flood. Therefore, there is a 0% chance that the value of the house will drop to $o. Conversely, there is a 100% chance that the house will retain its full value.

Step (5)

The expected costs of each event occurring given that you did and did not build a seawall is calculated as the loss in the expected value of your house. Since your house is worth originally worth $800,000, we can find the expected costs with and without a seawall follows by taking the difference between $800,000 and the house's expected value at each instance as follows:

The expected Costs and without a sea well is calculated above:

Step (6)

There is not enough information provided regarding the pricing of annual premiums for the house. We cannot find the cost of an insurance policy that offers full insurance nor a policy that pays only 75% of the home value. However, different policies should provide an incentive to be safer because if you knew that you would only receive a payment worth 75% of your house ($800,000.0.75 = $600,000) rather than a full payment of $800,000, you would be more careful in protecting your house against possible floods to minimize your expected costs.