ANSWER ALL THREE PROBLEMS. YOU MUST SHOW ALL YOUR WORK TO RECEIVE CREDIT.

Problem 1 (Decision Tree based)

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 (positive earnings), then a sequel will 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 were a flop i.e., is losing money, then no sequel would be produced. Use S for successful and F for flop or failure.

Draw a decision tree to analyze this problem and answer the following questions.

(a). What is the expected value of selecting script #1?

(b). What is the expected value of selecting script #2?