Question: Burt pays $30 a year for towing insurance. He thinks that the probability that he will need to have his car towed once in the next year is 1/10 and the probability that he will have to have it towed more than once is zero. It will cost $100 if his car is towed if he doesn't have insurance but will cost nothing if he does have insurance. Let X = Burt's cost next year for towing and/or insurance.
a. If Burt buys the insurance, X has only one possible value. What is it?
b. If Burt doesn't buy the insurance, X has two possible values. List the two values and their probabilities.
c. Refer to parts (a) and (b). In each case, find E(X). Using these two values for E(X), explain whether or not Burt should buy the insurance.