2,4,6,8,10
ER 4 Probability 4-3 Basic Skills and Concepts Statistical Literacy and Critical Thinking 1. Language: Complement of "At Least One" Let A = the event of getting at least one defective iPhone when 3 iPhones are randomly selected with replacement from a batch. Write a statement describing event A. 2. Probability of At Least One Let A = the event of getting at least I defective iPhone when 3 iPhones are randomly selected with replacement from a batch. If 5% of the iPhones in a batch are defective and the other 95% are all good, which of the following are correct? a. P(A) = (0.95) (0.95) (0.95) = 0.857 b. P(A) = 1 - (0.95) (0.95) (0.95) = 0.143 C. P(A) = (0.05) (0.05) (0.05) = 0.000125 3. Notation When selecting one of your Facebook Friends, let event F = female and let event H = high school classmate. Use your own words to translate the notation P( H | F ) into a ver- bal statement. 4. Confusion of the Inverse Using the same events F and H described in Exercise 3, describe confusion of the inverse. At Least One. In Exercises 5-12, find the probability. 5. Three Girls Find the probability that when a couple has three children, at least one of them is a girl. (Assume that boys and girls are equally likely.) 6. Probability of a Girl Assuming that boys and girls are equally likely, find the probability of a couple having a boy when their third child is born, given that the first two children were both girls. 7. Births in the United States In the United States, the true probability of a baby being a boy is 0.512 (based on the data available at this writing). Among the next six randomly selected births in the United States, what is the probability that at least one of them is a girl? out or 8. Births in China In China, where many couples were allowed to have only one child, the probability of a baby being a boy was 0.545. Among six randomly selected births in China, what is the probability that at least one of them is a girl? Could this system continue to work indefinitely? (Phasing out of this policy was begun in 2015.) 9. Phone Survey Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the prob- ability that for one such phone number, the last four digits include at least one 0. 10. At Least One Correct Answer If you make random guesses for 10 multiple choice SAT test questions (each with five possible answers), what is the probability of getting at least 1 correct? If these questions are part of a practice test and an instructor says that you must get at least one correct answer before continuing, is there a good chance you will continue? 11. At Least One Defective iPhone It has been reported that 20% of iPhones manufactured by Foxconn for a product launch did not meet Apple's quality standards. An engineer needs at least one defective iPhone so she can try to identify the problem(s). If she randomly selects 15 iPhones from a very large batch, what is the probability that she will get at least 1 that is defec- tive? Is that probability high enough so that she can be reasonably sure of getting a defect for her work? 12. Wi-Fi Based on a poll conducted through the e-edition of USA Today, 67% of Internet users are more careful about personal information when using a public Wi-Fi hotspot. What is the
