Diana has a car whose value is 40 thousand dollars. The probability of an accident is 10% and she will lose the car at occurrence of the accident. Diana has wealth of 20 thousand dollars aside from the car, and her utility over wealth is given by u (w) = w'2. Final wealth w is measured in thousands (for example, to = 60 if there is no accident and no other payment). 7. Suppose the insurance company decides the premium for full insurance is $12K. In addition, they also provide a partial insurance plan with a premium $6K. With partial insurance, they would pay half of Diana's loss in case of accident. Consider the following statements: (I) Diana prefers full insurance than partial insurance. (II) The insurance company's expected prots is lower with full insurance. (III) Suppose Diana overestimates the probability of car accidents. That is, she believes the probability of loss is p > 0.1 instead of 0.1. If p is suiciently close to 1, then she will choose partial insurance. (a) More than one statement are correct. (b) None of the statements is correct. (0) Only statement (I) is true. (d) Only statement (II) is true. (e) Only statement (III) is true