An engineer decided to make a careful analysis of the cost of fire insurance for his $200,000 home. From a fire rating bureau he found the following risk of fire loss in any year. Outcome Probability
No fire loss 0.986
$ 10,000 fire loss 0.010
$ 40,000 fire loss 0.003
$ 200,000 fire loss 0.001
(a) Compute his expected fire loss in any year.
(b) He finds that the expected fire loss in any year is less than the $550 annual cost of fire insurance. In fact, an insurance agent explains that this is always true. Nevertheless, the engineer buys fire insurance. Explain why this is or is not a logical decision.
