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 $400,000 that is located on a river. If the river floods? moderately, the house will be completely destroyed. This happens about once every 50 years. If you build a seawall, the river would have to flood heavily to destroy your house, which only happens about once every 100 years. What would be the annual premium without a seawall for an insurance policy that offers full? insurance? Without a seawall, the annual premium is ?$ . ?(Round your response to the nearest whole? number.) $8,000 What would be the annual premium with a seawall for an insurance policy that offers full? insurance? With a seawall, the annual premium is ?$ . ?(Round your response to the nearest whole? number.)$4,000

For a policy that only pays 80?% 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 80?% 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.)

Answer 1

With full insurance and without a seawall, the expected loss = worth of house * probability of house getting destroyed without a seawall

worth of house = $400,000

probability of house getting destroyed without a seawall = 1 / 50 = 0.02 year

With full insurance and without a seawall, the expected loss = $400,000 * 0.02 = $8,000

With full insurance and with a seawall, the expected loss = worth of house * probability of house getting destroyed with a seawall

worth of house = $400,000

probability of house getting destroyed with a seawall = 1 / 100 = 0.01

With full insurance and with a seawall, the expected loss = $400,000 * .01 = $4,000

so, the insurance charged by the insurance company is $8,000 without a seawall and with a seawall it is $4,000

without seawall annual premium would be 400000/50= 8000 per year

with a seawall annual premium would be 400000/100= 4000 per year to offer full insurance

for policy that pays 80% premium, expected cost without seawall is .80*400000/50 = 6400

with a seawall .80*400000/100= 3200

yes