### In how many ways can five different keys be put on a key ring?

In how many ways can five different keys be put on a key ring? [2] A particular airline has 10:00 a.m. flights from San Francisco to New York, Atlanta, and Miami. The probabilities that each flight is full are 0.60, 0.40, and 0.50 respectively, and each flight is independent one another. What is the probability that exactly one flight is full? [3] There is a saying about initial public offerings (IPOs) of stock: “If you want it, you can’t get it; if you can get it, you don’t want it.” This is because 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 probability of the stock performing well is 0.80. Overall, assume that you can obtain shares in about 15% of IPOs. Find the probability that the stock turned out not to perform well if you were unable to obtain such shares. What percentage of the time, over the long run, will you be pleased with the outcome? [4] In a past presidential election, the actual voter turnout was 61%. In a survey, 1002 subjects were asked if they voted in the presidential election. a) Find the mean and standard deviation for the number of actual voters in groups of 1002. b) In the survey of 1002 people, 701 said that they voted in the last presidential election (based on data from ICR Research Group). Is this result consistent with the actual voter turnout, or is this result unlikely to occur with an actual voter turnout of 61%? Why or why not? c) Based on these results, does it appear that accurate voting results can be obtained by asking voters how they acted? a.) What is the chance that finishers complete the run with the times between 50 and 70 minutes? b.) What is the chance that finishers complete the run with the times more than 75 minutes? c.) How fast do finishers have to complete the run among the top 5% finishers? Among them, 19 patients experienced flu symptoms and 844 patients did not (based on data from Pfizer, Inc.). a.) Estimate the probability that a patient taking the drug will experience flu symptoms. b.) Is this unusual to find that among 863 patients, there are 19 who experience flu symptoms in a)? Explain.

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