CHAPTER 11 Review Exercises 755 11.1–11.10 1. In your own words, explain the law of large numbers. Answers will vary. 2. Explain how empirical probability can be used to determine whether a die is “loaded” (not a fair die). Answers will vary. 3. Phones Of 45 people who purchase a phone at an electronics store, 40 purchased a smartphone. Determine the empirical probability that the next person who purchases a phone from that store purchases a smartphone. 8 9 4. Cards Draw one card from a standard 52-card deck 40 times with replacement and compute the empirical probability of selecting a heart. Answers will vary. 5. Television News In a small town, 250 people were asked whether they watched ABC, CBS, NBC, Fox, or MSNBC news. The results are indicated below. Network Number of People ABC 80 CBS 35 NBC 60 Fox 35 MSNBC 40 Determine the empirical probability that the next person randomly selected from the town watches ABC news. 8 25 Digits In Exercises 6–9, each of the digits 0 1 2 3 4 5 , , , , , , 6 7 8 9 , , , is written on a piece of paper and all the pieces of paper are placed in a hat. One number is randomly selected. Determine the probability that the number selected is 6. even. 1 2 7. odd or greater than 3. 4 5 8. greater than 2 or less than 6. 1 9. even and greater than 4. 1 5 Cheese Preference In Exercises 10–13, a taste test is given to 60 customers at a supermarket. The customers are asked to taste 4 types of cheese and to list their favorite. The results are summarized below. Type Number of People Cheddar 21 Monterey Jack 17 Gouda 13 Mozzarella 9 Review Exercises CHAPTER 11 If one person who participated in the taste test is randomly selected, determine the probability that the person’s favorite cheese was 10. cheddar. 7 20 11. Gouda. 13 60 12. either cheddar or Monterey Jack. 19 30 13. a cheese other than mozzarella. 17 20 14. High Blood Pressure According to the U.S. Centers for Disease Control and Prevention, 31% of adults in the United States have high blood pressure. If an adult was randomly selected, determine the odds a) against the adult having high blood pressure. 69 : 31 b) in favor of the adult having high blood pressure. 31 : 69 15. Vegetable Mix-up Nicholas, a mischievous child, has removed labels on the eight cans of vegetables in the cabinet. Nicholas’s father knows that there are three cans of corn, three cans of beans, and two cans of carrots. If the father randomly selects and opens one can, determine the odds against his selecting a can of corn. 5 : 3 16. Horseracing The odds against Fedora winning the Triple Crown in horse racing are 82 : 3. Determine the probability that Fedora wins the Triple Crown. 3 85 17. Pizza Restaurant Success The probability that a new pizza restaurant will succeed at a given location is 0.75. Determine the odds in favor of the pizza restaurant succeeding. 3 : 1 18. Raffle Tickets One thousand raffle tickets are sold at $2 each. Three prizes of $200 and two prizes of $100 will be awarded. Assume that the probability that any given ticket is selected for a $200 prize is 3 1000 and the probability that any given ticket is selected for a $100 prize is . 2 1000 a) Determine the expectation of a person who purchases a ticket. $1.20 − b) Determine the expectation of a person who purchases three tickets. $3.60 − 19. Expectation of a Card If Cameron selects a face card from a standard 52-card deck, Lindsey will give him $9. If Cameron does not select a face card, he must give Lindsey $3. a) Determine Cameron’s expectation. $0.23 − b) Determine Lindsey’s expectation. $0.23 c) If Cameron plays this game 100 times, how much can he expect to lose or gain? Lose $23.08
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