Problem 5 (Decision Analysis). You are considering investing $500,000 in a real estate project.
There is an 80% chance that you will make a profit of $300,000. But there is also a 20% chance that
you will loose $100,000.
(5.1) Easy. What is your expected profit if you invest?
(5.2) Moderate. Suppose you have the option of hiring the research firm RELCO, that can accurately
predict if the project will be successful, for a fee of $10,000. Should you hire RELCO?
Suppose RELCO is not always able to predict accurately. Based on historical performance,
RELCO predicts correctly 90% of the time when a project is successful; RELCO also predicts
correctly 90% of the time that a project is unsuccessful when this is the case.
(5.3) Moderate. Compute the probability that RELCO predicts a successful project.
Compute the probability that the project will be successful, given that RELCO predicts it
will be successful.
Compute the probability that the project will be successful, given that RELCO predicts it
will be unsuccessful.
(5.4) Challenging. Would you hire RELCO for $10,000?