$1)$ Investor A is an expected utility maximizer with a utility function U x x $()/=.$ Currently, Investor A is contemplating two investment opportunities, both with uncertain outcomes. Investment $1$ is a coin toss: the payoff can be either Y$1$ or Y$2$ dollars, each with probability $1/2.$ Investment $2$ is a roll of a fair six$-$sided die, and the payoff is Y$3$ dollars times the number that lands face up $(1$; $2$; $3$; $4$; $5$ or $6).$ Assume for simplicity that initial wealth is zero. $($a$)$ Which investment will Investor A choose using values for $12,,$ Y Y and Y$3,$ Gamma $=-2$

Y$1=$ $$10$

Y$2=$ $$60$

Y$3=$ $$10$

$($b$)$ Investor A $\text{'}$s friend Investor B is also contemplating the following two investment opportunities. Investment $1$ is a coin toss: the payoff can be either $$20$ or $$50,$ each with probability $1/2.$ Investment $2$ is a roll of a fair six$-$sided die, and the payoff is $$10$ times the number that lands face up $(1$; $2$; $3$; $4$; $5$ or $6).$ Assume for simplicity that initial wealth is zero. Like Investor A$,$ Investor B is a risk averse expected utility maximizer. Without knowing Investor B$\text{'}$s precise utility function, is it possible to tell which investment Investor B will choose? Explain why.