$5.$ The head of operations for a movie studio wants to determine which of two new scripts they should select for their next major production. $($Due to budgeting constraints, only one new picture can be undertaken at this time.$)$ She feels that script #$1$ has a $70$ percent chance of earning about $$10,000,000$ over the long run, but a $30$ percent chance of losing $$2,000,000.$ If this movie is successful, then a sequel could also be produced, with an $80$ percent chance of earning $$5,000,000,$ but a $20$ percent chance of losing $$1,000,000.$ On the other hand, she feels that script #$2$ has a $60$ percent chance of earning $$12,000,000,$ but a $40$ percent chance of losing $$3,000,000.$ If successful, its sequel would have a $50$ percent chance of earning $$8,000,000,$ but a $50$ percent chance of losing $$4,000,000.$ Of course, in either case, if the original movie was a "flop," then no sequel would be produced.

a$.$ What would be the total payoff if script #$1$ was a success, but its sequel was not?

b$.$ What is the probability that script #$1$ will be a success, but its sequel will not?

c$.$ What is the expected value of selecting script #$1?$

d$.$ What is the expected value of selecting script #$2?$

e$.$ Using expected monetary value, which alternative should be chosen? What is the expected value for the optimum decision alternativ

e$?$