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CHAPTER 5 PROBABILITY 378 81. Fill'er up! In a certain month, 88% of automobile 74. Middle school values Researchers carried out a survey P9869 drivers filled their vehicles with regular gasoline, 22 of fourth-, fifth-, and sixth-grade students in Michigan. purchased midgrade gas, and 10% bought premium Students were asked whether good grades, athletic abil gas. 20 Of those who bought regular gas, 28% paid with ity, or being popular was most important to them. The a credit card; of customers who bought midgrade and two-way table summarizes the survey data. $8 premium gas, 34% and 42%, respectively, paid with ; credit card. Suppose we select a customer at random Grade 4th 5th 6th Total (a) Draw a tree diagram to model this random process, 50 69 168 Grades 49 (b) Find the probability that the customer paid with a 98 Mos Athletic 24 36 38 credit card. important 22 69 Popular 19 28 135 335 (c) Suppose the chosen customer paid with a credit card Total 92 108 What's the probability that the customer bought Suppose we select one of these students at random. premium gas? (a) Find Pathletic | 5th grade). 82. Media usage and good grades The Kaiser Family (b) Use your answer from part (a) to help determine if the Foundation released a study about the influence of media events "5th grade" and "athletic" are independent. in the lives of young people aged 8- 18.2 In the study, 17% of the youth were classified as light media users, 62% 75. Rolling dice Suppose you roll two fair, six-sided dice- were classified as moderate media users, and 21% were one red and one green. Are the events "sum is 7" and classified as heavy media users. Of the light users who "green die shows a 4" independent? Justify your answer. responded, 74% described their grades as good (A's and (See Figure 5.2 on page 342 for the sample space of B's), while only 68% of the moderate users and 52% of the this random process.) heavy users described their grades as good. Suppose that 76. Rolling dice Suppose you roll two fair, six-sided dice- we select one young person from the study at random. one red and one green. Are the events "sum is 8" and "green die shows a 4" independent? Justify your answer. (a) Draw a tree diagram to model this random process. (See Figure 5.2 on page 342 for the sample space of this random process.) (b) Find the probability that this person describes his or her grades as good. 77. Free downloads? Illegal music downloading is a big pg 1366 problem: 29% of Internet users download music files, (c) Suppose the chosen person describes his or her grades and 67% of downloaders say they don't care if the as good. What's the probability that he or she is a heavy music is copyrighted. "Find the probability that a user of media? randomly selected Internet user downloads music and doesn't care if it's copyrighted. 83. First serve Tennis great Andy Murray made 60% of pg 370 his first serves in a recent season. When Murray made 78. At the gym Suppose that 10% of adults belong to his first serve, he won 76% of the points. When Mur- health clubs, and 40% of these health club members go ray missed his first serve and had to serve again, he to the club at least twice a week. Find the probability won only 54% of the points. Suppose you randomly that a randomly selected adult belongs to a health club and goes there at least twice a week. choose a point on which Murray served. You get dis- tracted before seeing his first serve but look up in time 79. Box of chocolates According to Forrest Gump, to see Murray win the point. What's the probability that "Life is like a box of chocolates. You never know he missed his first serve? what you're gonna get." Suppose a candymaker offers a special "Gump box" with 20 chocolate can- 84. Lactose intolerance Lactose intolerance causes dies that look alike. In fact, 14 of the candies have difficulty in digesting dairy products that contain lactose soft centers and 6 have hard centers. Suppose you (milk sugar). It is particularly common among people choose 3 of the candies from a Gump box at ran- of African and Asian ancestry. In the United States dom. Find the probability that all three candies have soft centers. not including other groups and people who consider themselves to belong to more than one race), 82% of 80. Sampling students A statistics class with 30 students the population is White, 14% is Black, and 4% is Asian has 10 males and 20 females. Suppose you choose Moreover, 15% of Whites, 70% of Blacks, and 90% of 3 of the students in the class at random. Find the Asians are lactose intolerant. 23 probability that all three are female. uppose we select a U.S. person at random and find that the person is lactose intolerant. What's the probability that she or he is Asian! 85. HIV testing Enzyme immunoassay (EIA) tests are used to screen blood specimens for the presence of