Question 1008137: An insurance company has determined that in a certain region the probability of lightning striking a house in a given year is about 0.0004, and the average cost of repairs of lightning damage is $7000 per incident. The company charges $22 per year for lightning insurance.
(a) What is the company's expected value for the net income from each lightning insurance policy in one year?
(b) If the company has 100,000 lightning damage policies, what is the company's expected yearly income from lightning insurance?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the probability of an individual house being hit by lightning = .0004
the cost of repair to damage by lightning = 7000 on the average.
the expected cost per house is therefore .0004 * 7000 = 2.8
the insurance company charges 22 per year.
their expected value is 22 - 2.8 = 19.2 per house per year.
suppose they sell the insurance policy to 100,000 houses.
they will get revenue of 22 * 100,000 = 2,200,000.
if .0004 of those houses get hit by lightning, .0004 * 100000 = 40 houses get hit by lightning each year on the average.
their cost will be 40 * 7000 = 280,000.
their net revenue will be 2,200,000 - 280,000 = 1,920,000
divide that by 100,000 and you get a net of 19.2 per house.
numbers look good.
the company's expected income per house = 19.2.
their expected income from 100,000 houses = 1,920,000.
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