The probability that a management trainee will remain with a company is 0-60. The probability that an employee earns more than Dollar 10,000 per month is 0.50. The probability that an employee is a management trainee who remained with the company or who earns more than Dollar 10,000 per month is 0.70. What is the probability that an employee earns more than dollar 10,000 per month, given that he is a management trainee who stayed with the company?
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- Bob earn 60,000 a year and an accounting firm each year he receives Reyes Bob has determined that the probability that he receives a 10% raise is .7 the probability that he earns a 3% raise is .2 and the probability that he earns a 2% raise is .1 a competing company has offered Bob a similar position for 65,000 a year Bob wonders if he should take the new job or take his chances with his current job. a. Find the mathematical expectation of the dollar amount of his raise at his current job b.You and a coworker are assigned a team project on which your likelihood or a promotion will be decidedon. It is now the night before the project is due and neither has yet to start it. You both want toreceive a promotion next year, but you both also want to go to your company’s holiday party that night.Each of you wants to maximize his or her own happiness (likelihood of a promotion and mingling withyour colleagues “on the company’s dime”). If you both work, you deliver an outstanding presentation.If you both go to the party, your presentation is mediocre. If one parties and the other works, yourpresentation is above average. Partying increases happiness by 25 units. Working on the project addszero units to happiness. Happiness is also affected by your chance of a promotion, which is depends on howgood your project is. An outstanding presentation gives 40 units of happiness to each of you; an aboveaverage presentation gives 30 units of happiness; a mediocre presentation gives 10 units…When playing roulette at a casino, a gambler is trying to decide whether to bet $10 on the number 30 or to bet $10 that the outcome is any one of the three possibilities 00, 0, or 1. 3 The gambler knows that the expected value of the $10 bet for a single number is - 53¢. For the $10 bet that the outcome is 00, 0, or 1, there is a probability of 38 of making a net profit of $30 and a probability of losing $10. 35 38 a. Find the expected value for the $10 bet that the outcome is 00, 0, or 1. b. Which bet is better: a $10 bet on the number 30 or a $10 bet that the outcome is any one of the numbers 00, 0, or 1? Why? a. The expected value is $. (Round to the nearest cent as needed.) b. Since the expected value of the bet on the number 30 is C than the expected value for the bet that the outcome is 00, 0, or 1, the bet on is better.
- Suppose that the University of Alabama and Clemson are making spending decisions for theupcoming year. Assume that Alabama is currently spending $15 million on their recruiting andfacilities, and Clemson is spending $10 million. Each team has an additional $5 million to spendor keep as profits. If they both choose to not spend the additional $5 million then Alabama hasa 60% chance of getting the highest quality quarterback recruit to commit to them (getting thecommitment of the player is the goal). However, if they both choose to spend the additional $5million then there is a 57% chance that Alabama gets the high quality quarterback to commit. IfAlabama spends the additional $5 million but Clemson doesn’t then there is a 67% chanceAlabama gets the recruit. However, if Alabama does NOT spend the additional $5million butClemson does then there is a 50% change either team gets the recruit’s commitment. Setup thepayoff matrix and label the players, their strategies, and their payoffs, and…According to the Intern al Revenue Service, the mean tax refund for the year 2014 was $2800 Assu me the stan dard devlation I6 $450 an d that the amounts 1etunded follow a normal probability distribution. a. What percont of the refunde aro more th an $3,100? (Round the Intermediate velues to 2 decimal places. Round your answer to 2 decimal places) Percert 0.25 % b. What percent of the refun ds are more th an $3,100 but less th an $3.500? (Round the intermediete values to 2 dec imal places Round your ans wer to 2 decimal places) Peroert c. What percent of the retun ds are more th an $2,250 but less than $3.500? (Round the inter mediate val ues to 2 decimal places Round your answer to 2 decimal places) PeroartIf a risk‐averse individual owns a home worth $100,000, and that individual iswilling to pay a maximum of $1,000 for an annual fire insurance policy that covers theentire loss in the event of a fire, then we know that:A. There is a one percent chance that the home will be destroyed by fire inthe next yearB. There is a greater than a one percent chance that the home will bedestroyed by fire in the next yearC. There is less than a one percent chance that the home will be destroyedby fire in the next yearD. None of the above is correct
- Lela must decide to go on a winter trip to norway with the hope of seeing northern light would yield a utility level of 2,000 but she has only a 50% chance that they will show during the days of her trip. making the trip without seeing the lights would yield a utility level of 100 and there is 50 % chance of this happening. what is lela's expected utilty if show goes on the trip? a. 2,100 b.1,050 c.42 d.950Suppose Grace and Lisa are to go to dinner. Lisa is visiting Grace from outof town, and they are to meet at a local restaurant. When Lisa lived in town,they had two favorite restaurants: Bel Loc Diner and the Corner Stable. Ofcourse, Lisa’s information is out of date, but Grace knows which is betterthese days. Assume that the probability that the Bel Loc Diner is better isp > 1/2 and the probability that the Corner Stable is better is 1 - p. Naturedetermines which restaurant Grace thinks is better. Grace then sends amessage to Lisa, either “Let’s go to the Bel Loc Diner,” “Let’s go to theCorner Stable,” or “I don’t know [which is better].” Lisa receives the message, and then Grace and Lisa simultaneously decide which restaurant to go to. Payoffs are such that Grace and Lisa want to go to the same restaurant, but they prefer it to be the one that Grace thinks is better. More specifically, if, in fact, the Bel Loc Diner is better, then the payoffs from theiractions are as shown in the…9. The probability of a woman having a baby boy is 50% and that of having a girl is also 50% What is the probability that a woman who has three children will have three boys? of T. 10. Lebo has 3 blue pens, 2 red pens, 5 black pens and 2 pencils in his pencil case. a. What is the probability that he takes a black pen? b. What is the probability that he takes an item that is not a black pen? 11. One card is drawn from a deck of 52 cards. What is the probability that the card will be a. red or an ace? b. a king of hearts? Samsung Quad Camera Shot with my Galaxy. A2.1s
- 1. A woman with current wealth X has the opportunity to bet an amount on the o ccurrence of an event that she knows will occur with probability P. If she wager s W, she will received 2W, if the event occur and if it does not. Assume that t he Bernoulli utility function takes the form u(x) = -e-TX with r> 0. How much should she wager? Does her utility function exhibit CARA, DARA, IARA?Edwina, a commodities broker, has acquired an option tobuy 1,000 oz of gold at $50/oz. If she takes the option and ifCongress relaxes import quotas, she can sell the gold for$80/oz. If she takes the option and Congress does not relaxthe import quotas, however, the company will lose $10/oz. Edwina believes that there is a 50% chance that the governmentwill relax the quota. She also has the option of waiting untilCongress decides whether to relax the import quota. If sheadopts this strategy, however, there is a 70% chance that someother broker will have already taken the option.a If Edwina is risk-neutral, what should she do? b If Edwina’s utility function for a change x in her as-set position is given by u(x) (10,000 x)1/2, what should she do?a Suppose you are given a choice between thefollowing options:A1: Win $30 for sureA2: 80% chance of winning $45 and 20% chance ofA2: winning nothing B1: 25% chance of winning $30B2: 20% chance of winning $45Most people prefer A1 to A2 and B2 to B1. Explainwhy this behavior violates the assumption that decisionmakers maximize expected utility.b Now suppose you play the following game: You havea 75% chance of winning nothing and a 25% chance ofplaying the second stage of the game. If you reach thesecond stage, you have a choice of two options (C1 andC2), but your choice must be made now, before youreach the second stage.C1: Win $30 for sureC2: 80% chance of winning $45 13.5 Bayes’ Rule and Decision Trees 767Most people choose C1 over C2 and B2 to B1 (from part(a)). Explain why this again violates the assumption ofexpected utility maximization. Tversky and Kahneman(1981) speculate that most people are attracted to thesure $30 in the second stage, even though the secondstage may never be…