Please help me solve the three parts with an explanation on how to solve

Diana has a car whose value is $40K. The probability of an accident is 10% and she will lose the car at occurrence of the accident. Diana has wealth of $20K aside from the car1 and her utility over wealth is given by n (w) = w'2 (where w is measured in thousands). (a) Suppose that the premium for the full insurance is 12K. Dow Diana buy the insurance? (b) What is the highest premium that Diana is willing to pay for the full insurance? What is the expected prot for the insurance company if the premium is this value you calculated? (c) Now, suppose that company offers a partial insurance program that pays back only a half of the value of the car. Assuming the full insurance is still an option at full price P-M' = 12 like in item (a): does Diana purchase the partial insurance if the premium is Ppartinl = 6