Harry is in his last semester at UT and is thinking about taking a stats class before graduating. He has a decision to make:

enroll now, take another course instead, or delay enrollment until he gets his first prelim grades back.

If he enrolls and passes the course, he estimates his starting salary will increase by x = $30, 000. If he enrolls but fails, he will need to stay at UT for another semester with a tuition cost of $25, 000. If he chooses to delay his decision but ends up not taking the course, he will have missed the opportunity to take another course that is of interest and will need to take it online at a cost of $5, 000. The other course will not increase his salary. Judging from his knowledge in probability and statistics, Harry estimates that he can pass the course with probability p = 0.6. Based on previous years' statistics, out of the students who passed, 0.8 fraction got a good grade on the first prelim, i.e. P(good grade on prelim | pass) = 0.8. On the other hand, out of the students who failed the course, 0.9 fraction got a bad grade on the first prelim, i.e. P(bad grade on prelim | fail) = 0.9. For simplicity, assume that Harry cannot drop the class once enrolled.

(a) (15 pts) Set up the decision tree.

(b) (25 pts) Compute the probabilities for all outcomes based on the information given above.

(c) (10 pts) Compute the expected values for each decision node. What is the associated optimal strategy at each decision node (specify which decision to take)?

(d) (10 pts) What is the minimum value of x for Harry to be willing to enroll immediately?