A home owner is considering insuring contents of his house against theft for one year. He approximates that the contents of his house would cost him $40,000 to replace. Local crime statistics point out that there is a probability of 0.03 that his house will be broken in the coming year. In that event his losses would be 10%, 20%, or 40% of the contents with probabilities 0.5, 0.35 and 0.15 respectively.
An insurance policy from company A costs $300 a year but guarantees to replace any losses because of theft. An insurance policy from company B is cheaper at $200 a year but householder has to pay the first $X of any loss himself. An insurance policy from company C is even cheaper at $150 a year but only replaces the fraction (Y%) of any loss suffered.
Suppose that there can be at most one theft a year.
A. Draw decision tree.
B. What would be your advice to the home owner if X = 50 and Y = 40% ?