Please explain in details how to find the answer to part c

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 car, and her utility over wealth is given by u (w) = -w'2 (where w is measured in thousands). (a) Suppose that the premium for the full insurance is 12K. Does Diana buy the insurance? (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 pfu = 12 like in item (a): does Diana purchase the partial insurance if the premium is PW'M' = 6