142 CHAPTER 3 Probability Finding Classical Probabilities In Exercises 41–46, a probability experiment consists of rolling a 12-sided die numbered 1 to 12. Find the probability of the event. 41. Event A: rolling a 2 42. Event B: rolling a 10 43. Event C: rolling a number greater than 4 44. Event D: rolling a number less than 8 45. Event E: rolling a number divisible by 3 46. Event F: rolling a number divisible by 5 Finding Empirical Probabilities A survey asked U.S. adults how many tattoos they have. The frequency distribution at the left shows the results. In Exercises 47 and 48, use the frequency distribution. (Source: Ipsos) 47. What is the probability that the next person asked does not have a tattoo? 48. What is the probability that the next person asked has two tattoos? Using a Frequency Distribution to Find Probabilities In Exercises 49– 52, use the frequency distribution at the left, which shows the population of the United States by age group, to find the probability that a U.S. resident chosen at random is in the age range. (Source: U.S. Census Bureau) 49. 18 to 24 years old 50. 25 to 44 years old 51. 45 to 64 years old 52. 65 years old and older Classifying Types of Probability In Exercises 53–58, classify the statement as an example of classical probability, empirical probability, or subjective probability. Explain your reasoning. 53. According to company records, the probability that an automobile will need covered repairs during its three-year warranty period is 0.46. 54. The probability of choosing 6 numbers from 1 to 40 that match the 6 numbers drawn by a state lottery is 1>3,838,380 ≈ 0.00000026. 55. An analyst feels that the probability of a team winning an upcoming game is 60%. 56. According to a survey, the probability that a randomly chosen high school counselor will say that significant changes are needed in U.S. schools is 55%. 57. The probability that a randomly selected number from 1 to 100 is divisible by 6 is 0.16. 58. You estimate that the probability of getting all the classes you want on your next schedule is about 25%. Finding the Probability of the Complement of an Event The age distribution of the residents of Ithaca, New York, is shown at the left. In Exercises 59–62, find the probability of the event. (Source: U.S. Census Bureau) 59. Event A: A randomly chosen resident of Ithaca is not 18 to 24 years old. 60. Event B: A randomly chosen resident of Ithaca is not 25 to 39 years old. 61. Event C: A randomly chosen resident of Ithaca is not less than 18 years old. 62. Event D: A randomly chosen resident of Ithaca is not 70 years old or older. Ages Frequency, f 0 –17 2416 18 –24 16,598 25 – 39 5293 40 –54 2726 55 –69 2140 70 and over 1396 TABLE FOR EXERCISES 59–62 Ages Frequency, f (in millions) Under 18 73.0 18 to 24 30.2 25 to 44 87.6 45 to 64 83.3 65 and over 54.1 TABLE FOR EXERCISES 49–52 Response Number of times, f None 704 One 131 Two 57 Three 34 Four or more 79 TABLE FOR EXERCISES 47 AND 48
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