Concept explainers
Prisoner’s dilemma. Two people are suspected of robbing a bank. They are being interrogated in separate rooms. If both stay silent, they can be conv icted of a lesser crime and sentenced to only 6 months. If one confesses (or “defects”) and the other does not, the confessor goes free as a reward for cooperating while the other suspect will be sent to prison for 10 years. If both defect, they each go to prison for 5 years. Create a payoff matrix from the point of view of Suspect #1. (Adopt the method from previous Mindscapes.)
Want to see the full answer?
Check out a sample textbook solutionChapter 8 Solutions
HEART OF MATHEMATICS
Additional Math Textbook Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Elementary and Intermediate Algebra: Concepts and Applications (7th Edition)
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Pre-Algebra Student Edition
Elementary Statistics: Picturing the World (7th Edition)
- Ben has a single-minded goal in life. He will have succeeded in reaching his goal if he receives a payoff of x that's 7 or more, He is allowed to choose between Gamble A: a single coin toss paying either 0 or 2a; or Gamble B: the sum of two coin tosses paying either 0 or a. In Gamble B, Ben's payoffs could be 0 if the two coin flips are both tails; a if one flip is heads and the other is tails; or 2a if both flips are heads. Gambles A and B have the same expected value. But A is riskier (more volatile or spread out) than B. Assume that Ben is an expected utility maximizer. State whether Ben maximizes expected utility by choosing risky A or 'less risky B in the two cases where a = 6 and a =8. Choose the best answer describing the choices that Ben will make: O A when a = 6 and A when a = 8 O B when a =6 and B when a = 8 O A when a = 8 and B when a=6 O B when a = 8 and A when a = 6 O A when a -6 and indifferent between A and B when a 8 O Indifferent between A and B when a 6 and B when a 8arrow_forwardSuppose a company charges a premium of $150 per year for an insurance policy for storm damage to roofs. Actuarial studies show that in case of a storm, the insurance company will pay out an average of $8000 for damage to a composition shingle roof and an average of $12,000 for damage to a shake roof. They also determine that out of every 10,000 policies, there are 7 claims per year made on composition shingle roofs and 11 claims per year made on shake roofs. What is the company’s expected value (i.e., expected profit) per year of a storm insurance policy? What annual profit can the company expect if it issues 1000 such policies? Determine the probability of a composition shingle roof claim out of 10,000 = ______ Determine the probability of a shake roof claim out of 10,000 = ______ How many claims are made out of 10,000? = _______ What is the probability of no claims out of 10,000? = _______ How much does each shingle roof claim cost the company, don’t forget each person pays $150…arrow_forwardThis game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…arrow_forward
- This game is called “Get Negative”. Roll two dice (record these in the order you roll them), and then do then do the following: take the first number rolled and subtract 2 times the second number rolled. Regardless of who rolls, Player A gets 3 points if the product is greater than or equal to 0 (i.e. it is zero or positive); Otherwise Player B gets 1 points. The players may or may not take turns rolling the dice as it does not matter who is rolling. Any player may score on any roll, and every roll will result in a score. Play the game by rolling the dice 25 times. For each turn, keep a record of both dice and the resulting answer and the points scored, according to the rules above. Tally the points and calculate the final score for each player. Remember, someone gets a point for each turn, depending on the numbers rolled. (One does not have to be rolling to receive the points.) (Note: you may test the game by yourself by doing all of the 25 rolls yourself and just giving the…arrow_forward7. Suppose lightning strikes at an average of 1.4 strikes per minute during a particular storm. You play the following game: if the next strike occurs within the next minute, you win 3 dollars, if the next strike occurs between 1 minute and 2 minutes from now, you win 5 dollars, and if the next strike occurs more than 2 minutes from now, you win 1 dollar. How much should someone be charged to play this game, to make it a "fair game?" Ans: $3.25arrow_forward2. A company makes electronic doohickeys. Seventeen out of every 80 doohickeys are faulty, but the company doesn't know which ones are faulty until a buyer complains. Suppose a doohickey costs $33 to make and they sell it for $55. This means the company makes a $22 profit on the sale of any working doohickey, but suffers a loss of $75 for every doohickey that is faulty because they have an amazing guarantee and will repair the unit. How much is the expected value of each doohickey? Can the company expect a profit in the long term? How much profit will they make if they sell 100 doohickeys? How much overall profit will they make if they sell 2000?arrow_forward
- The game of craps is played as follows: a player rolls two dice. If the sum is 2, 3, or 12, the player loses; if the sum is either a 7 or an 11, the player wins. If the outcome is anything else, the player continues to roll the dice until he rolls either the initial outcome or a 7. If the 7 comes first the player loses, whereas if the initial outcome reoccurs before the 7 appears, the player wins. Compute the probability of a player winning at craps.arrow_forwardPanaderio Bakery is getting more and more orders for durian pies. The bakers made 6 durian pies in June, 12 durian pies in July, 18 durian pies in August, and 24 durian pies in September. If this pattern continues, how many durian pies will the bakery make in October?arrow_forwardThe player pays a fee of $5 to play. The player then rolls a 12-sided die three times. If the player rolls a 7 on any of the three rolls, they win a prize. The prize is determined by the number of 7s rolled. If the player rolls one 7, they win $5. If the player rolls two 7s, they win a $10. If the player rolls three 7s, they win $20. Compare the theoretical results of the game to the experimental results, including a discussion of whether the results were typical or rare. Theoretical results: Roll (including all 3 rolls) Result Money earned 1 7,7,7 $15 2 2,4,5 $5 3 5,7,9 $5 4 1,9,3 $0 5 2,12,7 $5 6 3,12,3 $0 7 7,4,8 $5 8 6,7,7 $10 9 5,12,4 $0 10 7,5,7 $10 Experimental results: Roll (including all 3 rolls) Result Money earned 1 1,3,7 $5 2 3,6,4 $0 3 7,6,9 $5 4 8,7,7 $10 5 11,4,1 $0 6 6,5,7 $7 7 4,6,3 $0 8 7,1,9 $7 9…arrow_forward
- You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to roll a six-sided die. She will give you $4 times the number that appears on the die. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $5 if the spinner lands on blue and $15 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take. The expected value for your sister's game: $$ The expected value for your mother's game: $$ Which offer should you take?arrow_forwardA group of six friends are playing poker one night, and one of the friends decides to try out a new game. They are using a standard 52-card deck. The dealer is going to deal the cards face up. There will be a round of betting after everyone gets one card. Another round of betting after each player gets a second card, etc. Once a total of 7 cards have been dealt to each player, the player with the best hand will win. However, if any player is dealt one of the designated cards, the dealer collects all cards, shuffles, and starts over. The designated cards are: 9 of Hearts, Jack of Diamonds. The players wish to determine the likelihood of actually getting to play a hand without mucking the cards and starting over. In how many ways can you deal the cards WITHOUT getting one of the designated cards? (Hint: Consider how may cards are in the deck that are NOT one of the designated cards and consider how many cards need to be dealt in order for each player to have 7 cards.) In how many ways…arrow_forwardAt roulette, there are 38 slots. A "column" consists of 12 of these slots. A column pays 2 to 1. So, if you risk $1 on a column and win, you net gain +2 dollars. If you lose, your net equals –1 dollar. Suppose you will play for 100 rounds and bet one dollar on a column each round. (You may enter values rounded to the nearest cent. Beware of carried rounding error.) Your average net gain per play equals 0.0526 dollars. The SD of your net gain per play equals 1.39 dollars. The expected value of your total net gain after 100 plays equals -5.3 dollars. The standard error of your total net gain after 100 plays equals 13.94 dollars.arrow_forward
- Discrete Mathematics and Its Applications ( 8th I...MathISBN:9781259676512Author:Kenneth H RosenPublisher:McGraw-Hill EducationMathematics for Elementary Teachers with Activiti...MathISBN:9780134392790Author:Beckmann, SybillaPublisher:PEARSON
- Thinking Mathematically (7th Edition)MathISBN:9780134683713Author:Robert F. BlitzerPublisher:PEARSONDiscrete Mathematics With ApplicationsMathISBN:9781337694193Author:EPP, Susanna S.Publisher:Cengage Learning,Pathways To Math Literacy (looseleaf)MathISBN:9781259985607Author:David Sobecki Professor, Brian A. MercerPublisher:McGraw-Hill Education