686 CHAPTER 11 Probability Solution We use the formula = + = − + = Fair price expected value cost to play 1.50 4.00 2.50 Thus, the fair price to play this game would be $2.50. If the cost to play was $2.50 instead of $4.00, the expected value would be $0. ■ Now try Exercise 43 Instructor Resources for Section 11.3 in MyLab Math • Objective-Level Videos 11.3 • StatCrunch: Simulation: Raffle Winnings • PowerPoint Lecture Slides 11.3 • MyLab Exercises and Assignments 11.3 Exercises Warm Up Exercises In Exercises 1– 4, fill in the blank with an appropriate word, phrase, or symbol(s). 1. The expected gain or loss of an experiment over the long run is called the _______ value. Expected 2. In an experiment, if there is a loss in the long run, the expected value is _______. Negative 3. In an experiment, if there is a gain in the long run, the expected value is _______. Positive 4. In an experiment, if there is neither a gain nor a loss in the long run, the expected value is _______. 0 Practice the Skills/Problem Solving 5. Selling Hot Dogs An outdoor hot dog vendor sells an average of 60 hot dogs per day in dry weather and an average of 20 per day in rainy weather. If the weather in this area is rainy 20% of the time, determine the expected number of hot dogs sold per day. 52 hot dogs 6. Tax Law Changes Jonalynn, an investment counselor, is advising her client on a particular investment. She estimates that if the tax law does not change, the client will make $15,000 but if the tax law changes, the client will lose $4000. Determine the client’s expected value if there is a 20% chance the tax law will change. $11,200 7. Investment Club The Triple L investment club is considering purchasing a certain stock. After considerable research, the club members determine that there is a 70% chance of making $15,000, a 10% chance of breaking even, and a 20% chance of losing $8500. Determine the expectation of this purchase. $8800 8. Antiques Business Zelda is opening an antiques shop. In the first year, she estimates that there is a 25% chance that she will make $20,000, a 40% chance that she will break even, and a 35% chance that she will lose $30,000. Determine Zelda’s expected value for the first year of her business. −$5500 9. Corn Stalk Growth In July in Benton Township, corn stalks grow 2.5 in. per day on sunny days and 1.5 in. per day on cloudy days. If in Benton Township in July, 70% of the days are sunny and 30% are cloudy, a) determine the expected amount of corn stalk growth on a typical day in July in Benton Township. 2.2 in. b) determine the expected amount of corn stalk growth in July in Benton Township. 68.2 in. 10. Seattle Greenery In July in Seattle, the grass grows 1 2 in. a day on a sunny day and 1 4 in. a day on a cloudy day. If in Seattle in July, 75% of the days are sunny and 25% are cloudy a) determine the expected amount of grass growth on a typical day in July in Seattle. 7 16 in., or 0.4375 in. b) determine the expected total grass growth in the month of July in Seattle. 217 16 in., or 13.5625 in. 11. Fortune Cookies At the Pan Pacific restaurant, fortune cookies contain a slip of paper indicating a dollar amount that will be subtracted from your restaurant bill. You are to randomly select one out of ten fortune cookies. Of the ten cookies, seven contain “$1 off,” two contain “$2 off,” and one contains “$5 off.” If your restaurant bill was $45, determine a) the expected dollar amount to be deducted from your bill. $1.60 b) the expected dollar amount you will pay for your meal. $43.40 Alexey Stiop/Shutterstock SECTION 11.3
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