Consider the following decision tree where the firm can choose either option $\text{'}$a$\text{'}$ or option $\text{'}$b$\text{'}.$

The values c$,$ d$,$ e$,$ f and g are the probabilities this branch of the tree occurs. In this decision tree they all have the value of $0\mathrm{.}2.$

If the firm selects option $\text{'}$a$\text{'}$ and C occurs, the firm obtains a utility of $100.$ If D occurs it obtains $50.$ If E occurs it obtains a utility of $0.$ If the firm selects option $\text{'}$b$\text{'}$ it obtains a utility of $50$ if F occurs and $25$ if G occurs.

The expected utility of node A is thus Answer $1$ Question $1$

and the expected utility of node B is Answer $2$ Question $1$

$.$ The firm should select option Answer $3$ Question $1$

and the expected utility for the box P is Answer $4$ Question $1$