1. Explain why Bayes' theorem is necessary for handling additional information in a decision problem.

2. Explain the meaning of the term predictive probability.

3. For Example 15-4, suppose that hiring the economic consultants costs only $100,000 (in 10-years-after dollars). Redo the analysis. What is the optimal decision? Explain.

4. For problem, suppose that before deciding whether to advertise on television, the company can test the commercial. The test costs $300,000 and has the following reliability. If sales volume would go up by $20 million, the test would indi- cate this with probability 0.96. It would wrongly indicate that sales would be $10 mil- lion more with probability 0.03, and wrongly indicate that sales would be $1 million more with probability 0.01. If sales would increase by $10 million, the test would indi- cate this with probability 0.90, and the other two (wrong) possibilities with probability 0.05 each. The test would indicate that sales would rise by $1 million with probability 0.80 if that was really to happen, and wrongly indicate the other two possibilities with probability 0.1 each. Redo the decision problem.