176 CHAPTER 3 Probability 39. Zoning Board The Saratoga Springs, New York, Zoning Board of Appeals has seven members. One member serves as board chair and another serves as vice chair. Given the names of the seven board members, what is the probability of randomly selecting the name of the chair and the name of the vice chair? (Source: City of Saratoga Springs) 40. Board of Directors The University of Colorado Board of Directors has 23 members. One member serves as board chair and another serves as vice chair. Given the names of the 23 board members, what is the probability of randomly selecting the name of the chair and the name of the vice chair? (Source: University of Colorado) 41. Horse Race A horse race has 10 entries. Given no information about the horses or jockeys, what is the probability of randomly selecting (in no particular order) the first three horses to finish the race? 42. Pizza Toppings A pizza shop offers nine toppings. No topping is used more than once. What is the probability that a random choice of three toppings is sausage, onions, and green peppers? 43. Shuffle Play You use a shuffle playback feature to randomly play songs in a playlist. The playlist of 56 songs includes 15 instrumental songs. (a) What is the probability that the first three songs to play are instrumental songs? (Assume a song cannot be repeated.) (b) What is the probability that the first three songs to play are not instrumental songs? (Assume a song cannot be repeated.) 44. Officers The offices of president, vice president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team. (a) What is the probability that all of the offices are filled by members of the debate team? (b) What is the probability that none of the offices are filled by members of the debate team? Finding New Music In Exercises 45–48, use the pie chart, which shows the results of a survey of 513 music listeners who were asked about their primary source for new music. (Source: The Sound of AI) 45. You choose two music listeners at random. What is the probability that both say their primary source for new music is someone’s playlist? 46. You choose three music listeners at random. What is the probability that all three say their primary source for new music is subscription music services? 47. You choose nine music listeners at random. What is the probability that none of them say their primary source for new music is friends or social media? 48. You choose five music listeners at random. What is the probability that none of them say their primary source for new music is personal search? 49. Lottery In a state lottery, you must correctly select 5 numbers (in any order) out of 40 to win the top prize. You purchase one lottery ticket. What is the probability that you will win the top prize? Subscription music services Friends or social media Someone’s playlist 3.7% Other Primary Source for New Music Personal search 45.9% 26.1% 15.8% 8.4% FIGURE FOR EXERCISES 45–48
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