Jerry Smith $($see Problem $3-36)$ has done some analysis about the profitability of the bicycle shop. If Jerry

builds the large bicycle shop, he will earn $$60,000$ if

the market is favorable, but he will lose $$40,000$ if the

market is unfavorable. The small shop will return a

$$30,000$ profit in a favorable market and a $$10,000$

loss in an unfavorable market. At the present time, he

believes that there is a $5050$ chance that the market

will be favorable. His old marketing professor will

charge him $$5,000$ for the marketing research. It is estimated that there is a $0\mathrm{.}6$ probability that the survey

will be favorable. Furthermore, there is a $0\mathrm{.}9$ probability that the market will be favorable given a favorable outcome from the study. However, the marketing

professor has warned Jerry that there is only a probability of $0\mathrm{.}12$ of a favorable market if the marketing

research results are not favorable. Jerry is confused.