# Probability applied to economics

The following two questions are based on the wondrous Statistical topic probability. After attempting both questions I have yet to answer either correctly. If anyone has encountered similar problems before and understands how each is answered, I would be wholly appreciative if you could provide a systematic breakdown of how to do either, or both if possible.

1. A publisher sends advertising materials for an accounting text to 80% of all professors teaching the appropriate accounting course. Thirty percent of the professors who received this material adopted the book, as did 10% of the professors who did not receive the material. What is the probability that a professor who adopts the book has received the advertising material?

2. A stock market analyst examined the prospects of the shares of a large number of corporations when the performance of these stocks was investigated one year later, it turned out that 25% performed much better that the market average, 25%, much worse and the remaining 50%, about the same as the average. Forty percent of the stocks that turned out to do much better than the market were rated good buys by the analyst, as were 20% of those that did about as well as the market and 10% of those that did much worse. What is the probability that a stock rated a good buy by the analyst performed much better than the average?

You have 2 classifications - sent/not-sent (S/NS for short) and adopted/not-adopted (A/NA). That makes your underlying population split into 4 categories: (S,A), (S,NA), (NS,A), (NS,NA). First, using the data in the book, figure out the percentages corresponding to each. (E.g. that he sent it to 80% tells you that $(S,A) + (S,NA) = 0.8$ and $(NS,A)+(NA,NA) = 1-.8 = .2$. Figure out exactly what is the value of each of the 4 sub-classes.)
Then, you are looking for $$\mathbb{P}[S|A] = \frac{\mathbb{P}[S \text{ and } A]}{\mathbb{P}[A]} = \frac{(S,A)}{(S,A) + (NS,A)}.$$
• @ScottGoddard but the problem says that "$30\%$ of the professors who received this material adopted the book", so $(S,A) = 0.3 \times 0.8 = 0.24$! – gt6989b Apr 9 '14 at 20:00