756 CHAPTER 11 Probability 20. Expected Attendance If the day is sunny, 1000 people will attend the baseball game. If the day is cloudy, only 500 people will attend. If it rains, only 100 people will attend. The local meteorologist states that the probability of a sunny day is 0.4, of a cloudy day is 0.5, and of a rainy day is 0.1. Determine the number of people that are expected to attend. 660 people 21. Fair Price At a game of chance, the expected value is determined to be $2.50, − and the cost to play the game is $6.50. Determine the fair price to play the game. $4.00 22. Fair Price The expected value when you purchase a lottery ticket is $1.50, − and the cost of the lottery ticket is $5.00. Determine the fair price of the lottery ticket. $3.50 23. Club Officers Tina, Jake, Gina, and Carla form a club. They plan to select a president and a vice president. a) Construct a tree diagram showing all the possible outcomes. * b) List the sample space. * c) Determine the probability that Gina is selected president and Jake is selected vice president. 1 12 24. A Coin and a Number A coin is tossed and then a number from 1 through 4 is randomly selected from a bag. a) Construct a tree diagram showing all the possible outcomes. * b) List the sample space. * c) Determine the probability that a head is tossed and an odd number is selected. 1 4 d) Determine the probability that a head is tossed or an odd number is selected. 3 4 Spinning Two Wheels In Exercises 25–30, the outer and inner wheels are spun. Assuming that the wheels are independent and the sectors are equally likely, determine the probability of obtaining 25. even numbers on both wheels. 1 4 26. numbers greater than 5 on both wheels. 9 64 27. an odd number on the outer wheel and a number less than 6 on the inner wheel. 5 16 28. an even number or a number less than 6 on the outer wheel. 7 8 29. an even number or a color other than green on the inner wheel. 1 30. gold on the outer wheel and a color other than gold on the inner wheel. 3 16 Soft Drink Selection In Exercises 31–34, assume that Sonya is going to purchase three bottles of soft drinks at a store. The store has 12 different bottles of soft drinks, including 5 different bottles of cola, 4 different bottles of root beer, and 3 different bottles of ginger ale. If she randomly selects 3 of these bottles, determine the probability she selects 31. 3 bottles of cola. 1 22 32. no bottles of root beer. 14 55 33. at least one bottle of root beer. 41 55 34. a bottle of cola, a bottle of root beer, and a bottle of ginger ale in that order. 1 22 Spinner Probabilities In Exercises 35–38, assume that the spinner cannot land on a line. If spun once, determine 35. the probability that the spinner does not land on green. 5 8 36. the odds in favor of and the odds against the spinner landing on green. In favor, 3 : 5; against, 5 : 3 37. A person wins $10 if the spinner lands on green, wins $5 if the spinner lands on red, and loses $20 if the spinner lands on yellow. Determine the expectation of a person who plays this game. $3.75 38. If the spinner is spun three times, determine the probability that at least one spin lands on red. 7 8 Restaurant Service In Exercises 39 – 42, use the results of a survey regarding the service at the Lake View Diner, which is summarized as follows. Meal Service Rated Good Service Rated Poor Total Breakfast 95 15 110 Lunch 75 15 90 Total 170 30 200 *See Instructor Answer Appendix 1 2 3 4 5 6 7 8 8 2 7 6 5 1 4 3
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