3. Consider two projects that you can invest in: project A pays $100 with certainty, while project B pays $200 with probability 0.1, $80 with probability 0.6, and $50 with probability 0.3. Your utility is of the type U(x) = ax x2. You know that you are indifferent between the choice of receiving $1,000 for sure, or $2,000 and $400 with a fifty-fifty chance. Find your a, and decide which project you like better