Question: It is not necessary to have someone else set up a series of bets against you in order for incoherence to take its toll. It is conceivable that one could inadvertently get oneself into a no-win situation through inattention to certain details and the resulting incoherence, as this problem shows.

Suppose that an executive of a venture-capital investment firm is trying to decide how to allocate his funds among three different projects, each of which requires a $100,000 investment. The projects are such that one of the three will definitely succeed, but it is not possible for more than one to succeed. Looking at each project as an investment, the anticipated payoff is good, but not wonderful. If a project succeeds, the payoff will be a net gain of $150,000. Of course, if the project fails, he loses all of the money invested in that project. Because he feels as though he knows nothing about whether a project will succeed or fail, he assigns a probability of 0.5 that each project will succeed, and he decides to invest in each project.

1. According to his assessed probabilities, what is the expected profit for each project?
2. What are the possible outcomes of the three investments, and how much will he make in each case.
3. Do you think he invested wisely? Can you explain why he is in such a predicament?
4. If you feel you know nothing about some event, is it reasonable to assess equal probabilities for the outcomes? Give an example where this might be reasonable and another where it might not.

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Solution: The downloadable solution consists of 2 pages
Deliverable: Word Document