Your boss has asked you to work up a simulation model to examine the uncertainty re- garding the success or failure of five different investment projects. He provides probabil- ities for the success of each project individually: p1  = 0.50, p2  = 0.35, p3  = 0.65, p4 = 0.58, p5 = 0.45. Because the projects are run by different people in different seg ments of the investment market, you both agree that it is reasonable to believe that, given these probabilities, the outcomes of the projects are independent. He points out, however, that he really is not fully confident in these probabilities and that he could be off by as much as 0.05 in either direction on any given probability.

a. How can you incorporate his uncertainty about the probabilities into your simulation?

b. Now suppose he says that if he is optimistic about the success of one project, he is likely to be optimistic about the others as well. For your simulation, this means that if one of the probabilities increases, the others also are likely to increase. How might you incorporate this information into your simulation?