13. In a product liability case, a company can settle out of court for a loss of $350,000, or go to trial, losing $700,000 if found 23. Describe a situation in which a business can use expected guilty and nothing if found not guilty. Lawyers for the value. be 0.8. company estimate the probability of a not-guilty verdict to 24. If the expected value of a game is negative, what does this mean? Also describe the meaning of a positive and a zero a. Find the expected value of the amount the company can expected value. lose by taking the case to court. 25. The expected value for purchasing a ticket in a raffle is b. Should the company settle out of court? -$0.75. Describe what this means. Will a person who purchases a ticket lose $0.75? 14. A service that repairs air conditioners sells maintenance agreements for $80 a year. The average cost for repairing an Critical Thinking Exercises air conditioner is $350 and 1 in every 100 people who Make Sense? In Exercises 26-29, determine whether each statement purchase maintenance agreements have air conditioners makes sense or does not make sense, and explain your reasoning. that require repair, Find the service's expected profit per maintenance agreement 26. I found the expected value for the number of boys for a family with five children to be 2.5. I must have made an error because family with 2.5 boys cannot occur. Exercises 15-19 involve computing expected values in games of chance 27. Here's my dilemma: I can accept a $1000 bill or play a dice game ten times. For each roll of the single die, 15. A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than I win $500 for rolling 1 or 2. 1, the player wins nothing. If there is a charge of $1 to play . I win $200 for rolling 3. the game, what is the game's expected value? What does this . I lose $300 for rolling 4, 5, or 6. value mean? Based on expected value, I should accept the $1000 16. A game is played using one die. If the die is rolled and shows bill 1, the player wins $1; if 2, the player wins $2; if 3, the player 28. I've lost a fortune playing roulette, so I'm bound to reduce wins $3. If the die shows 4, 5, or 6, the player wins nothing. If my losses if I play the game a little longer. there is a charge of $1.25 to play the game, what is the game's expected value? What does this value mean? 29. My expected value in a state lottery game is $7.50. 17. Another option in a roulette game (see Example 6 on page 30. A popular state lottery is the 5/35 lottery, played in Arizona, 663) is to bet $1 on red. (There are 18 red compartments, Connecticut, Illinois, Iowa, Kentucky, Maine, Massachusetts, 18 black compartments, and 2 compartments that are neither New Hampshire, South Dakota, and Vermont. In Arizona's red nor black.) If the ball lands on red, you get to keep the $1 version of the game, prizes are set: First prize is $50,000, that you paid to play the game and you are awarded $1. If second prize is $500, and third prize is $5. To win first prize, the ball lands elsewhere, you are awarded nothing and the $1 you must select all five of the winning numbers, numbered that you bet is collected. Find the expected value for playing from 1 to 35. Second prize is awarded to players who select any four of the five winning numbers, and third prize is roulette if you bet $1 on red. Describe what this number awarded to players who select any three of the winning means. numbers. The cost to purchase a lottery ticket is $1. Find the 18. The spinner on a wheel of fortune can land with an equal expected value of Arizona's "Fantasy Five" game, and chance on any one of ten regions. Three regions are red, four describe what this means in terms of buying a lottery ticket are blue, two are yellow, and one is green. A player wins $4 if over the long run. the spinner stops on red and $2 if it stops on green. The 31. Refer to the probabilities of dying at any given age on page player loses $2 if it stops on blue and $3 if it stops on yellow. 630 to solve this exercise. A 20-year-old woman wants to What is the expected value? What does this mean if the purchase a $200,000 one-year life insurance policy. What game is played ten times? should the insurance company charge the woman for the 19. For many years, organized crime ran a numbers game that policy if it wants an expected profit of $60? is now run legally by many state governments. The player selects a three-digit number from 000 to 999. There are Group Exercise 1000 such numbers. A bet of $1 is placed on a number, say number 115. If the number is selected, the player wins $500. 32. This activity is a group research project intended for people If any other number is selected, the player wins nothing interested in games of chance at casinos. The research should Find the expected value for this game and describe what culminate in a seminar on games of chance and their this means. expected values. The seminar is intended to last about 30 minutes and should result in an interesting and Writing in Mathematics informative presentation made to the entire class. 20. What does the expected value for the outcome of the roll of Each member of the group should research a game avail- a fair die represent? able at a typical casino. Describe the game to the class and compute its expected value. After each member has done 21. Explain how to find the expected value for the number of girls for a family with two children. What is the expected this, so that class members now have an idea of those games with the greatest and smallest house advantages, a final value? group member might want to research and present ways for 22. How do insurance companies use expected value to currently treating people whose addiction to these games determine what to charge for a policy? has caused their lives to swirl out of control