A decision tree is provided.

Payoff $($$ millions$)$

$5\mathrm{.}0$

$-3\mathrm{.}0$

$3\mathrm{.}0$

$0$

$1\mathrm{.}8$

$1\mathrm{.}0$

$8\mathrm{.}0$

$-1\mathrm{.}0$

$1\mathrm{.}0$

a$)$ Calculate Expected value $($EV$)$ at every node. Show all work.

b$)$ What is the optimum decision and EV$?$

c$)$ If your risk tolerance is $$0,$ what is the best decision and EV$?$