226 CHAPTER 4 Discrete Probability Distributions In Exercises 9 and 10, find the expected net gain to the player for one play of the game. 9. It costs $25 to bet on a horse race. The horse has a 1 8 chance of winning and a 1 4 chance of placing second or third. You win $125 if the horse wins and receive your money back if the horse places second or third. 10. A scratch-off lottery ticket costs $5. The table at the left shows the probability of winning various prizes on the ticket. Section 4.2 In Exercises 11 and 12, determine whether the experiment is a binomial experiment. If it is, identify a success; specify the values of n, p, and q; and list the possible values of the random variable x. If it is not a binomial experiment, explain why. 11. Bags of milk chocolate M&M’s produced in the Hackettstown, New Jersey, factory contain 12.5% green candies. One candy is selected from each of 12 bags. The random variable represents the number of green candies selected. 12. A fair coin is tossed repeatedly until 15 heads are obtained. The random variable x counts the number of tosses. In Exercises 13–16, find the indicated binomial probabilities. If convenient, use technology or Table 2 in Appendix B. 13. Fifty-three percent of U.S. adults support attempting to land an astronaut on Mars. You randomly select eight U.S. adults. Find the probability that the number who support attempting to land an astronaut on Mars is (a) exactly three, (b) at least three, and (c) more than three. (Source: Gallup) 14. Forty-two percent of U.S. adults have a gun in their home. You randomly select 12 U.S. adults. Find the probability that the number who have a gun in their home is (a) exactly two, (b) at least two, and (c) more than two. (Source: Gallup) 15. Seventy-two percent of U.S. civilian employees have access to medical care benefits. You randomly select nine civilian employees. Find the probability that the number who have access to medical care benefits is (a) exactly six, (b) at least six, and (c) more than six. (Source: U.S. Bureau of Labor Statistics) 16. Sixty-two percent of candidates taking the Texas Bar Exam pass the test. You randomly select five Texas Bar Exam candidates. Find the probability that the number who pass is (a) exactly two, (b) at least two, and (c) more than two. (Source: National Conference of Bar Examiners) In Exercises 17 and 18, (a) construct a binomial distribution, (b) graph the binomial distribution using a histogram and describe its shape, and (c) identify any values of the random variable x that you would consider unusual. Explain your reasoning. 17. Seventy-two percent of U.S adults have read a book in any format in the past year. You randomly select five U.S adults and ask them whether they have read a book in any format in the past year. The random variable represents the number of adults who have read a book in any format in the past year. (Source: Pew Research) 18. Forty-nine percent of U.S adults answer correctly when asked “What is phishing?” You randomly select six U.S adults and ask them “What is phishing?” The random variable represents the number of adults who answer correctly. (Source: Proofpoint) Prize Probability $100,000 1 100,000 $100 1 100 $50 1 50 TABLE FOR EXERCISE 10
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