Question

Can someone do 28, 32, 40, and 44

198 CHAPTER 3 Probability c. Use the results of parts a and b to find ed value of Cash 4 admission to college); the Law School Admissions Test, or LSAT; and the Graduate Record Exam, GRE (used for admission to graduate school). 32. New York's "Pick 10" is a 10/80 lottery Sometimes, these maltiple-choice tests discourage guessing by subtracting points for wrong answers In particular, a correct answer will be worth +1 point and an incorrect answer on a question with five listed atraers (a through e) will be worth-a point. a Find the expected value of a random guess b Find the expectod value of climinating one answer and guessing among the remaining four possible are set; they do not vary with sales If ten winning numbers you win 3500,000 (but SI to play, so your profit is $499,999), If nine winning numbers, you win $6000. If you cight, seven, or six you win $300, S40 tively. If you match no winning numbers, you Otherwise, you lose your SI Find the probabilities of winning first prize, seo ond prize, and third prize b. Use the results of part a and the Complem Rule to find the probability of losing c. Use the results of parts a and b to find the expes ed value of Pick 10 Towers c Find the expected value of eliminating three answers and guessing between the remaining two Use decision theory and your answers to parts (a) d. (b), and (c) to create a guessing strategy for stan-33, Arizona and New York have Pick 3 games (Nw York's is called "Numbers"), as described in Exercises 19 and 20 of Section 3.4. If the player opts for "straight play" and wins, she wins $500 (but she pays $1 to play, so her profit is $499). If the playsr opts for "box play" with three different digits and wins, he wins $80. If the player opts for "box play" with two of the same digits and wins, he wins $160 dardized tests such as the SAT 28. a. Find the expected value of a S1 bet in six-spos keno if three winning spots pays S1 (but you pay $I to play, so you actually break even), four win- ning spots pays $3 (but you pay $1 to play, so your profit is $2), five pays $100, and six pays $2.600. (Use the probabilities computed in Exercise 16 of Section 3.4.) h Interpret the expected value Find the expected value of a $1 bet in eight-spos kno if four winning spots pays $1 (but you pay SI to play, so you actually break even), five win- ning spots pays S5 (but you pay $1 to play, so your prolit is $4), six pays $100, seven pays $1.480, and eight pays $19,000. (Use the proba- bilities computed in Exercise 17 of Soction 34.) h Interpret the expected value 31. a Find the ex keno if five wineing spots pays S1 (bet you pay S1 to play, so you actually break even), six win- ning spots pays $50 (but you pay $1 to play, so your profit is $49), seven pays $390, eight pays 6,000, and nine pays $25,000. (Use the peoba- biüities computed in Exercise IS of Section 34) s Isterpet the expected valur Ariaona's "Cash 4 is NUMBERS a. Use the probabilities from Exercises 19 and 20 of Section 3.4 to find the probability of losing b Use the probabilities from part a and from Exer cises 19 and 20 of Section 3.4 to find the expctd value of the game Write a paragraph in which you compare the states fiscal policies concerning their lotteries with the casinos' fiscal policies concerning their keno Assume that the expected value of a $1 lottery bet described in Exercises 31, 32, and/or 33 is represen tative of that of the other states' lotteries, and assume that the expected value of a $1 keno bet described in Exercises 28, 29, and/or 30 is re sentative of other keno bets expected value of a $1 bet in nine-spot 34. Section 3.4) a 4126 lottery. I: differs from doot vary at its payouts are set wtoring numbers, you win $10,000 (but you pay play soyour profis is $9999). If you match 35. Trustworthy Insurance Co. estimates that a certain home has a 1% chance of burning down in any one year. They calculate that it would cost $120,000 to rebuild that home. Use expected values to determine the annual insurance premium all you match two of the winning nusmbers, ber ou win S2. 3. Mr and Mas Trump hame applied to the Trastworthy Insurance Co. for insurance on Mrs. Trum diamond tiara. The tiara is valued at $97,500 Trustworthy estimates that the jewelry has a 2.3% chance of being stolen in any one year. Use expected values to determine the annual insurance premium. ood prine, and third prize h. Use the results of parts a and the Ralle to fied the probubility of losing of winning first prize, sec- The Black Gold Oil consid either in Jed Clampett's back yard oe his freet ard. After thorough testing and analnis, they estimate that there is a. 30% chance of striking oil in the back yard and a 40% chance in the front ard. They also estimate that the back yard site would either net $60 million if eil is found) or tose $6 million if oil is not found), and the fronttis lesons yard site would either net $40 million or lose s6 million. Us decision theory to dttermine where they should drill s. If in Exercise 37, Jed Clampett rejected the use of dinner for two a decision theory, where would he drill if he were an optimist? What would he do if he were a pessimist? 8. A community youth group is having a rafle to raise funds. Several community businesses have donated prizes The prizes and their retail value are copy o listed in Figure 3.33. Each prize will be given away regardless of the number of rafle tickets sold. ctning PTA mem Tickets are sold for $15 each. Determine the expected value of a ticket, and discuss whether it Co. is considering drilling 35 Exercises 199 Rutall Vale in Hawas, and airfare tion so an loternet one-year subecrip tion at the Centervile 5240 a f Centervile bers' Exvorite recipes would be to your financial advantage to buy igure M Data for ticket under the given circumstances a. 1000 tickets are sold. b. 2000 tickets are sold. Club is having a raffie to raise funds. Several com- munity basinesses have donated prizes. The prizes and their retaill value are listed in Figure 335. Each prize will be given away, regandless of the number of raffle tickets sold. Tickets are sold, for $5 each. Determine the expected value of a ticket, and disouss whether it would be to your financial advantage to buy a ticket umder the given circumstances a. 1000 tickets are sold b. 2000 tickets are sold. c. 3000 tickets are sold e. 3000 tickets are sold These Prizes to Retail Vale Be Given Away of Prize a cell phone and a one- ed year subscriptiom a one-year subscription to$500 an Iaternet service provider dinner for two at Spiedini's$100 Number of These Prizes to Be Glive Aay Retail Vae 20 SI80 a one-year subscription to the local newspaper Data for Exercise 39 Figure 3.33 20 CDs at Einstein 40. The Centerville High School PTA is having a raffle Entertainment to raise funds Several community basinesses have donated prizes The prizes and their retail value are listed in Figure 3.34. Each prize will be given away, Freddie's Pizza regardless of the number of raffle tickets sold Tickets are sold for $30 each. Determine the expect ed value of a ticket, and discuss whether it would be to your financial advantage to buy a ticket under the $23 a giant pizza and your choice of beverage at 15 520 a one-year subicription so the Young Repablican Figure 3.35 Data for Exercise 41 42. The Southern State University Ecology Club is having a raffle to raise funds Several community businesses have donated prizes The prizes and their 100 tickets are sold 200 tickets are sokd a. h. c. 300 tickets are sold. a. How many tickets would have to be you were playing cight-spot keno? b How much would it cost to parchase thee if each oosts $52 e. If it takes five seconds to parchase one tick the average keno game lasts twenty minute many people would it take to purchase the r number of tickets? 47. If you had $100 and were applying the marting strategy to the black-number bet in roulett you started with a $1 bet, how many losses could you afford? How large would your te profit be if you lost each bet except for the lau are listed in Figure 3.36. Each prize will rwxx regardless of the nummber of rafle Tickets are sold for $.30each. Determine espected svaloe of a ticket, and discuss whether t wowld be to your finan age to buy a oicket under the given circumstances these icko 100 ockets are sold XO tickets are sol. e 300 tickets are sold Namber of These Retail Pries to Be VleGivea Away one? 48. If you had $10,000 and were applying the martingle strategy to the black-number bet in roulcte and you started with a S1 bet, how many successive lose could you afford? How large would your net peofitbe if you lost each bet exceps for the last one? 52.990 Costa Ric ent$750 575 550 inswer the following questions asing complete sentences and your own words 20 Data for Eurose 42. ev" Lus 41 Find the expected value of theInternational Lotto Funds application of the "cover all of the numbers ■CONCEPT QUESTIONS of the concept of expect ed value to three different people: an ocasional gambler, a regular gambler, and a casino owner. To whom is the concept most meaningful? To wbom s it least meaningful? Why? 50. Discuss the advantages and disadvantages of deci- sion theory. Consider the application of decision thoory to a nonrecurring situation and to a recur ring situation. Also consder Jed Clampett and the Black Gold Ol Co. in Exercises 37 and 38 Assume that 55 million was spent on lottery tickets that half of the 513 million raised went for manage- ment expenses and that the balance was ne spest. Also assume that Virginia honors the win- sing ticket 44. One application of the "cover all the numbers" trategy would be to bet S1 on every single namber in roulette a Find the eults of this strategy How couks you use the expectod valuc of the S1 siage-number bet) to answer part (ay? S. The appliation of the "cover all the numbers" strat n to a molern state lottery would involve the 51. Design a game of chance. Use probabilities and HANDS ON punchase of a large number of tickets a How many tickets would harve to be purchased if you were in a state that has a 649 lottery (the player selects 6 out of 49 sumbers)? Now much would it cost to purchase these tickets i each costs $17 expected values to set the house odds so that the house will make a profit. However, be certain that your game is not so obviously pro-house that no one would be willing to play. Your project should include the following: , a complete description of how the game is played , a detailed mat hematical analysis of the expected value of the game for of each separate bet in the game, whichever is appropriate) a complete description of the betis) and the hous c. If you orpanized a group of 100 people to pur- chase these tickets and it takes one minute to purchase cach ticket, how many days would it take to ase the required number of tickets? the numbers" stral- 46. The application of the "cover all egy to Keno would involve the humber of tickets e purchase of a large 52. What lottery games are wailable where you live Choose one and find its expected value a larg

Answer 1

28)

consider a 1 bet in six spot keno and if three winning spots pay 1,four winning spot pays 3, five pays 100 and six pays 2600

out.come Plobubiity o,00012.0 0.00 306 loinnin spoks 0.018538 y inning spos 5 wnwing res 0.129010 Fe werthan oinin Using thi above .-theexre(ted value, dy beを 勿ould be

but this is less than the bet amount we are putting

So there is an expected loss of 0.860433 - 1 = -0.13956 = -0.14

b) Expected value is less than the given bet amount

So, expected loss will be = 0.8604 - 1 = -0.14

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