Maria is comparing three different insurance packages that would mitigate her medical costs for the upcoming year. She estimates that there is a 20% chance she will have a medical bill of $16,000, otherwise she will have to pay nothing. Her current wealth is $30,000. Her utility of wealth function is $U(w) = 2\sqrt{w}$. The three insurance options are detailed below, giving the per-dollar premium and amount of insurance.
Plan A: $0.25 premium on $16,000
Plan B: $0.25 premium on $12,000
Plan C: $0.20 premium on $8,000
What is Maria's expected utility if she buys no insurance?
Will Maria buy one of the insurance plans? If so, which one?