Option C: Cash4Life, Lucky4Life or similar (groups of 2): 1. Find the expected value without the lifetime prizes considered. 2. Find the expected value assuming the cash option will be selected rather than the annuity 3. Find the expected value if the annuity will be paid for 20 years. (minimum the lottery will pay out) 4. Find the expected value if the annuity will be paid for 50 years. 5. If none of the above values made buying a ticket "worth it" how long would you have to receive the annuity for the ticket to be "worth it"? For each of the above make sure to answer the question is it "worth it" to buy tickets?
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- You and your friends decide to play a game. You are rolling a die. If you roll a 6, you win $5. If you roll a 1, 3, or 5, you win $3. If you roll a 2, you win $4. If you roll a 4, you win $1. You only want to play the game if your expected payout is more than $3.50. Should you play the game? Show work to support the answer.Rolling two fair dice At the Spring Bazaar Charity Fundraiser, you play a game in which you roll two dice. (All proceeds go to the charity.) The game costs $1 to play. If you roll a sum of 2, you win $4. If you roll a sum greater than 2 and at most 4, you win $1. If you roll a sum of 11, you win $0.50. If you roll a sum of 12, you must donate an additional $1 to the charity. If you roll any other sum, the game is over.Complete the table to find the expected value of this game from the point of view of the Spring Bazaar Fundraising committee. Round all dollar values to two decimal places. Event Value Probability Value x Probability sum of 2 $ $ 2<sum< 4 $ $ $ $ $ $ $ $ Expected Value = $ ____________ per playThe Advantage Cash Card At the student union on a certain campus, you can save on food purchases by using the Advantage Cash Card. You deposit money into an Advantage Cash account and are issued a credit card the you use to purchase food. The card has several advantages: If you open your Advantage Cash account for 200 or more, a 5% bonus is added to your account balance. When you use your Advantage Cash Card, you receive 5% off the retail price of any food purchase. When you buy food with cash, you must pay a sales tax of 7.375%. With the Advantage Cash Card, you pay no sales tax. a.An item retails for 1.00. What do you pay if you use your Advantage Cash Card? b.An item retails for 1.00. What do you pay if you use cash? Round your answer to five decimal places for use in part d. c.What retail value of food will you be able to purchase if you open an Advantage Cash account for 300? Suggestion: Dont forget your 5% bonus and use the results of part a d.What retail value of food would you be able to purchase with 300 if you spend it as cash at the food court? Suggestion: Use the results of part b e.Calculate the percentage increase from your answer for part d to your answer for part c. Explain in practical terms the meaning of this percentage.
- Tiger Funds Ltd. operates a number of mutual funds in high technology and in financial sectors. Hussein Roberts is a fund manager who runs a major fund that includes a wide variety of technology stocks. As fund manager he decides which stocks should be purchased for the mutual fund. The compensation plan for fund managers includes a first-year bonus for each stock purchased by the manager that gains more than 10% in the first six months it is held. Of those stocks that the company holds, 40% are up in value after being held for two years. In reviewing the performance of Mr. Roberts, they found that he received a first-year bonus for 60% of the stocks that he purchased that were up after two years. He also received a first-year bonus for 40% of the stocks he purchased that were not up after two years.What is the probability that a stock will be up after two years given that Mr. Roberts received a first-year bonus?Olive Branch is a writer of romance novels. A movie company and a TV network both want exclusive rights to one of her most popular works. If she signs with the network she will receive a single lump sum, but if she signs with the movie company, the amount she will receive depends on the market response (box office) to the movie. Olive's payoffs are summarized: Box Office Small Medium Large Movie Company $200,000 1,000,000 3,000,000 TV network 900,000 900,000 900,000 Probability 0.3 0.6 0.1 1. Without any additional information, what is Olive’s best decision? Additionally, Olive may hire a market research firm to conduct a survey at a cost of $100,000. The result of the survey would be either a "F"avorable or an "U"nfavorable public response to the movie. The firm's historical accuracy, as measured by conditional probabilities is: P("F"|Small) = .3 P("U"|Small)…4. Filtering RedRocks Consulting Contributions RedRocks Consulting is a large computer consulting firm in Denver, Colorado. DonMcCubbrey, the CEO and founder of the firm, is well-known for his philanthropic efforts. Hebelieves that many of his employees also contribute to nonprofit organizations and wantsto reward them for their efforts while encouraging others to contribute to charities. Hestarted a program in which RedRocks Consulting matches 50 percent of each donation anemployee makes to the charity of his or her choice. The only guidelines are that the charity must be a nonprofit organization and the firm’s donation per employee may not exceed $500 a year.Don has started an Excel file, T3_RedRocks_Data.xls, to record the firm’s donations. Included in this file are the dates the request for a donation was submitted, the employee’sname and ID number, the name of the charity, the dollar amount contributed by the firm,and the date the contribution was sent. Don wants you to help him…
- 5. A farmer in Georgia must decide which crop to plant next year on his land: corn, peanuts, or soybeans. The return from each crop will be determined by whether a new trade bill with Russia passes the Senate. The profit the farmer will realize from each crop, given the two possible results on the trade bill, is shown in the following payoff table: Course Professor Fulton Ray Scott Crop Trade Bill Pass Fail Corn Peanuts Soybeans $35,000 $ 8,000 18,000 12,000 22,000 20,000 Determine the best crop to plant, using the following decision criteria. a. Hurwicz (a = .3) b. Equal likelihoodEverybody Wins Inc.: Everybody Wins Inc. (EWI) manufactures and sells several different board games online and through department stores nationwide. EWI's most popular game, Bunco Wars, is played with 5 six-sided dice. EWI has purchased dice for this game Gameplay Ltd. for twenty-five years, but the company is now considering a move to Diehard, Inc., a new supplier that has offered to sell dice to EWI at a substantially lower price. EWI management is intrigued by the potential savings offered by Diehard, but is also concerned about the quality of the dice produced by the new supplier. EWI has a reputation for high integrity, and its management feels that it is imperative that the dice included with Bunco Wars are fair. To alleviate concerns about the quality of the dice it produces, Diehard allows EWI's manager of product quality to randomly sample five dice from its most recent production run. While being observed by several members of the Diehard management team, EWI's manager of…After giving the lotto a try you decide to go back to Clayton Campus for some more gambling action. Theyare playing a die tossing game where you win a brand new home if you roll all sides of the die within 7rolls. Your crystal ball can see into the future and tells you that when you roll the die 7 times you don't seethe same number appear twice in a row. You decide to bet your entire rent for the year and try to win thehouse. You toss a fair six-sided die 7 times. Consider the following events, A = “each value appears atleast once” and B = “the outcome is alternate in numbers (i.e., a specific face of the die cannot be observed to occur directly after it was observed on the previous roll but it may have occurred elsewhere inthe sequence of rolls)”. What is p(A|B)? Are you likely to win the house?
- Portfolio Option 1: Tug of War DIRECTIONS: Use the information provided below about the first two rounds to figure out who will win the third round of tug of war. Round 1: One side of the rope there are four acrobats who all have equal strength. On the other side are five grandmas who each have equal strength as well. The result of the tug of war is dead even- it's a perfect tie Round 2: One one side is Ivan the dog. One the other side is are two grandmas and one acrobat. Again, it is dead even- a perfect tie. gOWNO Round 3: Three grandmas and Ivan are pulling against four acrobats. Which team wins? Justify your answer with at least 2 sentences. * FINAL ROUND * Round 4: Ivan and three acrobats are matched up against a team of grandmas. The result is a tie- the two sides are evenly matched. How many grandmas were on the the team? Explain your reasoning. Round 5: Create two teams of your choice in Round 5 that are not equally matched. Use Ivan and at least one acrobat and one grandma…A die is rolled. If an odd number turns up, we win an amount equal to this number; if an even number turns up, we lose an amount equal to this number. For example, if a two turns up we lose 2, and if a three comes up we win 3. What is the average profit you can make if you participate this game?Average profit isRound off your final answer into four decimal places. #.####7 Carl bets one dollar to play a game of 3 dice. If he rolls ”6” on one, two or three dice, then he takes the dollar back and win as many dollars as the number of dice which rolled ”6” (meaning 3 dollars max). If no die rolls a ”6”, Carl loses his bet. How much money is Carl expected to win if he continues playing this game numerous times? How much does Carl need to bet so in the long run he loses nothing and gains nothing