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- Deborah is at the casino and is considering playing Roulette. In Roulette, a ball drops into one of 36 slots on a spinning wheel. 17 of the slots are red, 17 are black, and 2 are green. Each slot is equally likely and occurs with probability 1/36. Deborah bets $1.00 on black. If the ball drops into a black slot she receives $2.00 and if it drops into a red or green slot, she receives nothing. a) The expected value of Deborah’s bet (after subtracting the $1.00 she bet) is $________________ b) Given that Deborah makes this bet, is she risk adverse, risk neutral, or risk loving?efer to the following table showing the probability distribution of payoffs from an activity to answer the question below: Units Payoff Probability 1 $30 10% 2 40 25% 3 60 30% 4 50 20% 5 10 15% What is the expected value?Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. What is expected gains/loss.
- "Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,480,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $203,000 is 0.27. The probability of a medium box office of $1,660,000 is 0.49, and the probability of a large box office of $2,950,000 is 0.24.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $20,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.75 probability the critic will have a favorable opinion.If the movie will have a medium…4.25 The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): State of Nature Low Demand Medium Demand High Demand Decision Alternative s1 s2 s3 Manufacture, d1 -20 40 100 Purchase, d2 10 45 70 The state-of-nature probabilities are P(s1) = 0.35, P(s2) = 0.35, and P(s3) = 0.30. Use a decision tree to recommend a decision.Recommended decision: Use EVPI to determine whether Gorman should attempt to obtain a better estimate of demand.EVPI: $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…
- For a group of 300 cars the numbers, classified by colour and country of manufacture, are shown in the table. Black Silver White Korea 33 34 35 Japan 23 9 24 America 16 25 34 Germany 19 16 32 One car is selected at random from this group. Find the probability that the selected car is a black or white car manufactured in Korea. not manufactured in Japan. is a white car, given that it was manufactured in America. Are the events ‘Korea’ and ‘Black’ Mutually Exclusive? Justify your response. Are the events ‘Korea’ and ‘Black’ Independent? Justify your response"Jay, a writer of novels, just has completed a new thriller novel. A movie company and a TV network both want exclusive rights to market his new title. If he signs with the network, he will receive a single lump sum of $1,460,000, but if he signs with the movie company, the amount he will receive depends on how successful the movie is at the box office.The probability of a small box office earning $210,000 is 0.27. The probability of a medium box office of $1,530,000 is 0.64, and the probability of a large box office of $3,190,000 is 0.09.Jay can send his novel to a prominent movie critic to assess the potential box office success. It will cost $21,000 to get the novel evaluated by the movie critic.The movie critic can have either a favorable or unfavorable opinion. The movie critic's reliability of predicting box office success is as follows.If the movie will have a large box office, there is a 0.61 probability the critic will have a favorable opinion.If the movie will have a medium…True/False a. Consider a strategic game, in which player i has two actions, a and b. Let s−i be some strategy profile of her opponents. If a IS a best response to s−i, then b is NOT a best response to s−i. b. Consider the same game in (a). If a IS NOT a best response to s−i, then a does NOT weakly dominates b. c. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, IS a best response to s−i, SO IS a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. d. Consider the same game in (a). If a mixed strategy of i that assigns probabilities 13 and 23 to a and b, respectively, is NOT a best response to some strategy profile of her opponents, s−i, NEITHER is a mixed strategy that assigns probabilities 32 and 13 to a and b, respectively. e. Consider the same game in (a). If a IS a best response to s−i, SO IS any mixed strategy that assigns positive probability to a. f. Consider the same game in (a). If a…
- 2.4 The opening 2018 World Cup odds against being the winning team specified by espn.com were 9/2 for Germany, 5/1 for Brazil, 11/2 for France, 20/1 for England, and 7/1 for Spain. Find the corresponding prior probabilities of winning for these five teams.2. Kier, in The scenario, wants to determine how each of the 3 companies will decide on possible new investments. He was able to determine the new investment pay off for each of the three choices as well as the probability of the two types of market. If a company will launch product 1, it will gain 50,000 if the market is successful and lose 50,000 if the market is a failure. If a company will launch product 2, it will gain 25,000 if the market is successful and lose 25,000 if the market will fail. If a company decides not to launch any of the product, it will not be affected whether the market will succeed or fail. There is a 56% probability that the market will succeed and 44% probability that the market will fail. What will be the companies decision based on EMV? What is the decision of each company based on expected utility value?6) For the payoff table below, the decision maker will use P(s1) = .15, P(s2) = .5, and P(s3) = .35. s1 s2 s3 d1 -5000 1000 10,000 d2 -15,000 -2000 40,000 (a) What alternative would be chosen according to expected value? (b) For a lottery having a payoff of 40,000 with probability p and -15,000 with probability (1-p), the decision maker expressed the following indifference probabilities. Payoff Probability 10,000 .85 1000 .60 -2000 .53 -5000 .50 Let U(40,000) = 10 and U(-15,000) = 0 and find the utility value for each payoff. (c) What alternative would be chosen according to expected utility?