# Subjective Probability of a Capital Investment Firm

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 .5 that each project will succeed, and 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?

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#### Solution Preview

1. The payoff according to him is as

-100,000 with probability 0.5 and +150,000 with probability 0.5

Expected profit for each project = ...

#### Solution Summary

This solution calculates the total expected payoff, the possible outcomes of success and failures and how much the firm loses.