Consider the following game tree, which has min $($down triangle$),$ max $($up triangle$)$ and chance

$($circle$)$ nodes. For the chance nodes the probability of each outcome is equally likely.

Figure $2$: Game Tree

a$)$ To find the value of $E$ in the game tree shown in figure $2,$ do you need to evaluate the value

of A and B$?$ Why or why not?

b$)$ To find the value of $E$ in the game tree shown in figure $2,$ do you need to evaluate the value

of $C$ and $D?$ Why or why not?

c$)$ If the value of $C=36$ and $D=26,$ then find the value of $F,G,H$ and $E$ nodes and show the

calculated values in figure $2.$