Use the information in Exercise 4.17 to answer this question. Suppose that every home is worth $100,000 and that an insurance company sells 1-year policies to every household for $500 that will pay either $100,000 or nothing, depending on whether the home is destroyed by fire.

a. Is the expected value of the amount the insurance company has to pay larger or smaller than $500?

b. For a Careless household, is the expected value of the payoff larger or smaller than

$500?

c. For a Careful household, is the expected value of the payoff larger or smaller than

$500?

d. What potential problem do you see for this insurance company?

Exercise 4.17

Suppose that there are two kinds of households, the Careless and the Careful; 99 percent of households are Careful and 1 percent are Careless. In any given year, a home inhabited by a Careless household has a 0.010 probability of being destroyed by fire, and a home occupied by a Careful household has a 0.001 probability of being destroyed by fire. If a home is destroyed by fire, what is the probability that it was occupied by a Careless household?