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.What is the probability of getting a king if a card is drawn from a pack of 52 cards?
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- Bob is playing 1/4 L + 3/4 R. What is Ann's expected payoff of playing D? Game Bob L RAnn U 10,-1 0, 1 D 4, 1 8, -12. 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?Question 4 Suppose a prosecutor expects to convict a defendant with probability 0.5 and that the sentence on conviction is 10 years in prison. Assume the prosecutor values prison time at $1,000 per year (its value as a deterrent of crime), and incurs a cost of trial equal to $2,000. a. What is the minimum prison sentence the prosecutor will o er as part of a plea bargain if her objective is to maximize the expected value of the sentence imposed, less the cost of trial (ignore the information provided in b. below to answer this question a.)? b. Suppose the defendant believes his chances of being convicted are 0.3, his cost of prison time is $5,000 per year, and his cost of a trial is $1,000. Will he accept the plea bargain in a.?
- 1. What is the expected value of playing this game ? a. The player repeatedly rolls a six - side d die until it comes up 6. b. When the die comes up 6 , the player receives a payoff, and the game ends. The player get s precise ly one payof f. c. The initial payoff is $6, and it increases by 20%. The f irst roll payoff is $6 ; the second roll payoff is $7.20 (1.2*$6) ; the third roll payoff is $8.64 (1.2*$7.20), and so on. What is the expected value of playing this game?Choice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work. (b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy? can you help me for par (b) plase?Choice under uncertainty. Consider a coin-toss game in which the player gets $30 if they win, and $5 if they lose. The probability of winning is 50%. (a) Alan is (just) willing to pay $15 to play this game. What is Alan’s attitude to risk? Show your work.(b) Assume a market with many identical Alans, who are all forced to pay $15 to play this coin-toss game. An insurer offers an insurance policy to protect the Alans from the risk. What would be the fair (zero profit) premium on this policy? i need help with question B please.
- In the final round of a TV game show, contestantshave a chance to increase their current winnings of$1 million to $2 million. If they are wrong, theirprize is decreased to $500,000. A contestant thinkshis guess will be right 50% of the time. Should heplay? What is the lowest probability of a correctguess that would make playing profitable?Your utility function is given by M1/2. You have $100 and are planning to invest in a venture where you can win or lose 50 with equal probability. Will you accept the venture? What is the minimum gain you need to make in the good scenario such that you will invest in the venture?6. Jerry plans to buy a new Bluetooth headset. He knows that the same product is offered in different shops with prices of $44, $49, and $60, and with odds of one-third of finding each price. He just stopped at a shop and knows that their price is $49. If the search cost is $1 per additional search, what should Jerry do?
- Jamal has a utility function U= W1/2 where Wis his wealth in millions of 'dollars and Uis the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1million with a probability of 0.6 and $9 million with a probability of 0.4. a. Graph Jamal's utility function. Is he risk-averse? Explain. b. Does A or B offer, Jamal, a higher expected price? Explain your reasoning with appropriate calculations. (Hint: The expected value of a random variable is the weighted average of the possible outcomes, where the probabilities are the weights.) c. Does A or B offer Jamal a higher expected utility? Again, show your calculations. d. Should Jamal pick A or B? Why?Consider the following variation to the Rock (R), Paper (P), Scissors (S) game:• Suppose that the Player 1 (row player) has a single type, Normal.• Player 2 (column player) has two types Normal and Simple.• A player of Normal type plays this zero-sum game as we studied in class whereas a player of type Simple always play P.• Player 2 knows whether he is Normal or Simple, but player 1does not.a) Suppose player 2 is of type Normal with probability 1/3 and of type Simple with probability (2/3). Find all pure strategy Bayesian Nash Equilibria.b) Suppose player 2 is of type Normal with probability 2/3 and of type Simple with probability (1/3). Find all pure strategy Bayesian Nash Equilibria.In a final round of a MegaMillion TV show, a contestant has won $1 millionand has a chance of doubling the reward. If he loses his winnings drop to$500,000. The contestant thinks his chances of winning are 50%. Should heplay? What is the lowest probability of a correct guess that will make his betprofitable? Show work
