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.)

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.)

Answer 1

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 years

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

2) 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