(a) Find the expected value (in dollars) of the amount won by one entry. (b) Find the expected value (in dollars) if the cost of entering this sweepstakes is the cost of a postage stamp (34 cents)
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Expected value of an event refers to the probable outcome of the event if all the possibilities and their their probability of happening are taken into consideration.
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- A friend offers you a chance to play a game in which there are only two outcomes, each with equal probability. If you get the "good" outcome, you win $80. But if you get the bad outcome, you only win $20. What price to play would make this a fair game (fair bet)? Carefully follow all mathematical instructions in your answer.1. Individual Problems 18-1 You hold an oral, or English, auction among three bidders. You estimate that each bidder has a value of either $88 or $110 for the item, and you attach probabilities to each value of 50%. The winning bidder must pay a price equal to the second highest bid. The following table lists the eight possible combinations for bidder values. Each combination is equally likely to occur. On the following table, indicate the price paid by the winning bidder. Combination Number Bidder 1 Value Bidder 2 Value Bidder 3 Value Probability Price ($) ($) ($) 1 $88 $88 $88 0.125 2 $88 $88 $110 0.125 3 $88 $110 $88 0.125 4 $88 $110 $110 0.125 5 $110 $88 $88 0.125 6 $110 $88 $110 0.125 7 $110 $110 $88 0.125 8 $110 $110 $110 0.125 The expected price paid is . Suppose that bidders 1 and 2 collude and would be willing to bid up to a maximum of their values, but the two bidders…1 . Individual Problems 17-2 You're a contestant on a TV game show. In the final round of the game, if contestants answer a question correctly, they will increase their current winnings of $3 million to $4 million. If they are wrong, their prize is decreased to $2,250,000. You believe you have a 25% chance of answering the question correctly. Ignoring your current winnings, your expected payoff from playing the final round of the game show is . Given that this is , you play the final round of the game. (Hint: Enter a negative sign if the expected payoff is negative.) The lowest probability of a correct guess that would make the guessing in the final round profitable (in expected value) is . (Hint: At what probability does playing the final round yield an expected value of zero?)
- 7) Manager B Effort Level Chance of success Cost of effort High Effort 0.6 100,000 Routine Effort 0.5 60,000 What is the minimum bonus that will entice high effort? 1. 40,000 2. 260,000 3. 300,000 4. 400,000 5. 520,000 6. 60,000 7. 100,000 8. 0 6) Manager A Effort Level Chance of success Cost of effort High Effort 0.6 300,000 Routine Effort 0.5 260,000 What is the minimum bonus that will entice high effort? 1. 40,000 2. 260,000 3. 300,000 4. 400,000 5. 520,000 6. 60,000 7. 100,000 8. 0 5) ABC Instrument, a manufacturer of precise scientific instruments, relies heavily on the efforts of its local salespeople. Selling an instrument requires either luck, high effort, or some combination of the two. A salesperson who chooses to work hard has a 40 percent chance of selling an instrument in a given year while a salesperson who chooses…1. A dealer decides to sell a rare book by means of an English auction with a reservation price of 54. There are two bidders. The dealer believes that there are only three possible values, 90, 54, and 45, that each bidder’s willingness to pay might take. Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other’s valuation. Assuming that the two bidders bid rationally and do not collude, the dealer’s expected revenue is approximately ______. 2. A seller knows that there are two bidders for the object he is selling. He believes that with probability 1/2, one has a buyer value of 5 and the other has a buyer value of 10 and with probability 1/2, one has a buyer value of 8 and the other has a buyer value of 15. He knows that bidders will want to buy the object so long as they can get it for their buyer value or less. He sells it in an English auction with a reserve price which he must…17-2 Game Show Uncertaninty In the final round of a TV game show, contestants have a chance to increase their current winnings of $1 million to $2 million. If they are wrong, their prize is decreased to $500,000. A contestant thinks his guess will be right 50% of the time. Should he play? What is the lowest probability of a correct guess that would make playing profitable?
- Please correct answer and don't use hend raitingYou are a hotel manager and you are considering four projects that yield different payoffs, depending upon whether there is an economic boom or a recession. The potential payoffs and corresponding payoffs are summarized in the accompanying table Project Red Orange Green Blue Multiple Choice The expected value of project Red is O OO $110. $50. $100. Boom (80%) $80 $ 70 $200. $90 $ 110 Recession (20%) $70 $80 $ 90 $ 110A lottery system has balls numbered 1 to 65 and randomly selects 6 of the lottery balls. There is only one prize of $ 10,000,000.00 which is awarded only it a lottery player selects the correct set of 6 lottery balls. a) If a lottery ticket costs $ 5.00, what is a lottery player's expected value? b) How much would the lottery prize have to be worth if it was to be a fair game? (Note: Include dollar signs in your answer)
- 12. Over the last decade, robotic-drone a research and development company has researched in new drone technology for home delivery. Their sales department considers that they could sell as many as $90 million per year with a probability of 20%. With a most likely value of $76 million with a probability of 45% and a lowest value of $50 million. a. Determine the expected value of their sales. b. The sales department estimates that they could maintain this sales rhythm for 4 years with a probability of 67% or that this sales rhythm could be maintained for 8 years. Determine the Expected Value for the PW if the company considers a yearly interest rate of 10%Please answer last 2 questions.190 ↑ 1. Individual Problems 17-1 Philippines You're the manager of global opportunities for a U.S. manufacturer that is considering expanding sales into Asia. Your market research has identified the market potential in Malaysia, the Philippines, and Singapore as described in the following table: Malaysia Probability Units Philippines Probability Units Singapore Probability Units Big 0.3 1,300,000 O Philippines O Singapore O Malaysia Success Level 0.7 1,100,000 0.5 600,000 Mediocre 0.3 650,000 0.1 352,000 0.3 360,000 Failure 0.4 0 0.2 0 0.2 0 The product sells for $30, and each unit has a constant marginal cost of $24. Assume that the (fixed) cost of entering the market (regardless of which market you select) is $750,000. In the following table, enter the expected number of units sold, and the expected profit, from entering each market. Market Expected Number of Units Sold Expected Profit Malaysia Philippines Singapore $ $ If you were to enter one of the previously described markets,…