PROBLEM $(3)$ Your bike is worth $$196.$ There is a probability of $\%50$ that you will have an accident that will cause $D of damage to your bike. You are an expected utility maximizer with $()=.($a$)$ There is a risk neutral insurance agency that insures you $-$in return for an insurance premium of $$96-$ against accident risk by fully compensating you for the damages, in case of an accident. What is the minimum level of damages D$,$ for which you would want to be insured? What is the maximum level of damages D$,$ for which the insurance company is willing to sell this insurance to you? $($b$)$ In $($a$),$ assume D $=160.$ Suppose that the insurance company offers an alternative insurance called $$half$-$coverage insurance$.$ This half insurance costs half as much $($$$96/2=$ $$48)$ but covers half of the damages in case of an accident. Would you prefer the original full insurance, half insurance or no insurance at all?