198 CHAPTER 4 Probability 11. Random Seats on Ryanair When four researchers checked into a Ryanair flight from Manchester to Dublin, there were 65 seats available, and 15 of them were middle seats (based on data from “How ‘Random’ is Ryanair’s Seating Allocation” by Jennifer Rogers, Significance). All four researchers were assigned middle seats. If the four researchers were assigned seats randomly, what is the probability that they are all given middle seats? What does the result suggest about Ryanair’s claim that seats are randomly assigned? 12. Vision Correction About 75% of the U.S. population uses some type of vision correction (such as glasses or contact lenses). a. If someone is randomly selected, what is the probability that he or she does not use vision correction? b. If four different people are randomly selected, what is the probability that they all use vision correction? c. What is the general criterion for using probability to determine whether a number of successes among n trials is significantly high? d. If you randomly select four people, is a result of all four using vision correction significantly high? Why or why not? 13. National Statistics Day a. If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in Japan. Ignore leap years. b. If a person is randomly selected, find the probability that his or her birthday is in October. Ignore leap years. c. Estimate a subjective probability for the event of randomly selecting an adult American and getting someone who knows that October 18 is National Statistics Day in Japan. d. If ten adult Americans are randomly selected and nine of them know that October 18 is National Statistics Day in Japan, is that result of nine significantly high? 14. Composite Sampling for Diabetes Currently, the rate for new cases of diabetes in a year is 4.3 per 1000 (based on data from the Centers for Disease Control and Prevention). When testing for the presence of diabetes, the Newport Diagnostics Laboratory saves money by combining blood samples for tests. The combined sample tests positive if at least one person has diabetes. If the combined sample tests positive, then the individual blood tests are performed. In a test for diabetes, blood samples from 10 randomly selected subjects are combined. Find the probability that the combined sample tests positive with at least 1 of the 10 people having diabetes. Is it likely that such combined samples test positive? 15. Texas Two Step In the Texas Two Step lottery, winning the top prize requires that you select the correct four different numbers from 1 to 35 (in any order and without replacement) and you must also select the correct additional “Bonus Ball” number between 1 and 35, which is drawn separately. The additional Bonus Ball number could be the same as one of the first four selected numbers. What is the probability of winning the top prize? (Express the answer as a fraction.) As this exercise was written, the jackpot was advertised to be $200,000; does that seem fair?
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