11.3 Expected Value (Expectation) 687 12. Clothing Sale At a special clothing sale at the Crescent Oaks Country Club, after the cashier rings up your purchase, you select a slip of paper from a box. The slip of paper indicates the dollar amount, either $5 or $10, that is deducted from your purchase price. The probability of selecting a slip indicating $5 is , 7 10 and the probability of selecting a slip indicating $10 is . 3 10 If your original purchase before you select the slip of paper is $200, determine a) the expected dollar amount to be deducted from your purchase. $6.50 b) the expected dollar amount you will pay for your purchase. $193.50 13. Black Chips and White Chips A bag contains 7 black chips and 3 white chips. Dexter and Thanh play the following game. Dexter randomly selects one chip from the bag. If the chip is black, Dexter gives Thanh $5. If the chip is white, Thanh gives Dexter $10. a) Determine Dexter’s expectation. −$0.50 b) Determine Thanh’s expectation. $0.50 14. Blue Chips and Red Chips A bag contains 4 blue chips and 6 red chips. Chi and Dolly play the following game. Chi selects one chip from the bag. If Chi selects a blue chip, Dolly gives Chi $6. If Chi selects a red chip, Chi gives Dolly $5. a) Determine Chi’s expectation. −$0.60 b) Determine Dolly’s expectation. $0.60 15. Roll a Die Alyssa and Gabriel play the following game. Alyssa rolls a die. If she rolls a 1, 2, or 3, Gabriel gives Alyssa $3. If Alyssa rolls a 4 or 5, Gabriel gives Alyssa $2. However, if Alyssa rolls a 6, she gives Gabriel $19. a) Determine Alyssa’s expectation. −$1 b) Determine Gabriel’s expectation. $1 16. Pick a Card Mike and Dave play the following game. Mike draws one card from a standard 52-card deck. If he draws an ace, Dave gives him $39. If not, he gives Dave $13. a) Determine Mike’s expectation. −$9 b) Determine Dave’s expectation. $9 17. Multiple-Choice Test A multiple-choice test has five possible answers for each question. For each correct answer, you are awarded 5 points. For each incorrect answer, 1 point is subtracted from your score. For answers left blank, no points are added or subtracted. a) If you do not know the correct answer to a particular question and you guess at the answer, determine your expectation. 1 5 b) If you do not know the correct answer to a particular question, is it to your advantage to guess? Explain. Yes, because you have a positive expectation of 1 5 c) If you do not know the correct answer but can eliminate one possible choice and then guess at the answer, determine your expectation. 1 2 d) If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Explain. Yes, because you have a positive expectation of 1 2 18. Multiple-Choice Exam A multiple-choice exam has four possible answers for each question. For each correct answer, you are awarded 5 points. For each incorrect answer, 2 points are subtracted from your score. For answers left blank, no points are added or subtracted. a) If you do not know the correct answer to a particular question and you guess at the answer, determine your expectation. 1 4 − b) If you do not know the correct answer to a particular question, is it to your advantage to guess? Explain. No, because you have a negative expectation of 1 4 − c) If you do not know the correct answer but can eliminate one possible choice and then guess at the answer, determine your expectation. 1 3 d) If you do not know the correct answer but can eliminate one possible choice, is it to your advantage to guess? Explain. Yes, because you have a positive expectation of 1 3 Spinners In Exercises 19 and 20, assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the person’s expectation. 19. $5 $10 $7.50 20. $10 $1 $5 $5.25 Spinners In Exercises 21 and 22, assume that a person spins the pointer and is awarded the amount indicated if the pointer points to a positive number but must pay the amount indicated if the pointer points to a negative Dmytro Zinkevych/ Shutterstock
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