Question: There is a saying about initial public offerings (IPOs) of stock: "If you want it, you cannot get it; if you can get it, you do not want it." The reason is that it is often difficult for the general public to obtain shares initially when a "hot" new company first goes on sale. Instead, most of us have to wait until it starts trading on the open market, often at a substantially higher price. Suppose that, given that you can obtain shares at the initial offering, the probability of the stock performing well is 0.35. However, given that you are unable to initially purchase shares, the conditional probability is 0.8 of performing well. Overall, assume that you can obtain shares in about 15% of IPOs.
a. Draw a probability tree for this situation.
b. Find the probability of both, (1) your being able to purchase the stock at the initial offering, and (2) the stock performing well.
c. How much access to successful IPOs do you have? Answer this by finding the conditional probability that you are able to purchase stock initially, given that the stock performs well.
d. What percentage of the time, over the long run, will you be pleased with the outcome? That is, either you were able to initially obtain shares that performed well, or else you were unable to obtain shares that turned out not to perform well.