Lucy and Henry each have $3108. Each knows that with 0.1 probability, they will lose 85% of their wealth. They both have the option of buying do units of insurance, with each unit costing $0.1. Each unit of insurance pays out $1 in the event the loss occurs. The cost of the insurance policy is paid regardless of whether the loss is incurred. Lucy's utility is given by uL(x)=qu(x)=x, Henry's utility is given by uH(x)=x\\luH(x)=x. Answer the following: Write your answers to 2 decimal places. a) Without insurance, what is the expected value of the loss? b) For Henry, facing the "lottery \" above without any insurance is as bad as losing how many dollars for sure? c) Find Lucy's utility maximising choice of do. If more than 1 exist, enter the largest do. d) Now suppose insurance costs $0.2. What is Lucy's utility maximising choice of do? e) What is Henry's utility maximising choice of do with the new price