I am having trouble figuring out the problem below. I have already calculated it, but want to make sure I am figuring it correctly. A health insurance company has identified two student risk groups (smokers and non-smokers) with healthcare costs given in the table below:

Group Healthcare cost Probability of getting sick Smokers $900 50% Non-smokers $900 20%

Each student has a monthly disposable income of $1000 and has a utility function given by U(x)=sqrt(x) where x is the student's disposable income after medical/health insurance expenses.a. Calculate the actuarially fair insurance premiums for the two groups (i.e. the expected cost of claims).b.Construct the lotteries associated with the students' disposable income (after health expenses) in the case without health insurance. Calculate the Expected Utility, the Certainty Equivalent and the Risk Premium associated with the lotteries for the two groups of students. c.Assume the company cannot price discriminate between the two groups of students. How should the company price (full) insurance contracts? Which group will purchase health insurance?