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 lo.......................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.