1.
A company is evaluating whether to market and sell product X. A previous in-house study has concluded that the probability of good sales is 1/4. The cost of bringing the product to market is 5. If the sales are good the company will make 105, otherwise it will lose 55. Some in the sales department are skeptical of X’s chances and suggest to cut one’s losses and not to market or sell the product at all, with a loss of 10. A market analysis with reliability of 80% is being considered to determine whether X will be successful. What is the maximum price the company should pay for it? [Answer: Less than 16]
2.
Your patient is very sick, and without any surgery she will die in 3 months. There is a risky operation that will extend her life to 10 months. However, the probability of death from such surgery is 1/4. There is a test which if positive increases the chances of surviving the operation; the test’s reliability is 9/10 for true positives and 8/10 for true negatives. The test is dangerous, as the patient might not survive it. What must be the probability of death from the test for you to advise your patient to take it? Assume that the patient’s utility is equal to her months of survival and that the utility of death is zero. [Answer: Greater than 8/11]