# bayes theorem and probability

A young engineer has invented holographic mobile phones and has approached a venture capital company to invest in it. The venture capital company considers the product to be an all or nothing product: either everyone will want one because everyone else has one or no one will want one because there will be no one to use it with. The company believes that the probability that it will take off netting them a profit of $2000000 is 0.14. If it doesn't take off then they expect that they would loose $200000. They are considering using a consumer survey to gather more information. However, the company has experience that shows that the probability that the consumer survey will predict success for a product that will fail is 0.24, and the probability that the consumer survey will predict failure when the product will be a success is 0.07. What is the monetary value of the information from a consumer survey to the venture capital company in this case? (ie what is the maximum that they should spend on a consumer survey)?

#### Solution Preview

See attached for the decision tree

See the formulas in the cells for the decision tree.

Steps:

1. Use bayes theorem to calculate the posterior probabilities that the survey will forecast a success and failure.

2. Use the bayes theorem to calculate the probabilities that products ...

#### Solution Summary

A decision tree and its calculations are provided in this solution. The bayes theorem is discussed in respect to probability of investments.