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
The Heart of Mathematics: An Invitation to Effective Thinking
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)
- You visit an island where three triplet brothers named Lanister, Lewis and Tom, live. They are indistinguishable in appearance, but Lanister and Lewis, are knaves whereas Tom is a knight. One day you meet one of the three on the street and wish to know whether or not he is Lewis, because Lewis owes you money. You are allowed to ask him only one yes/no question (your question may not have more than three words!) What question would work?Provide logical reasoning for your answerarrow_forwardBen 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_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_forwardIn 2004 it surfaced in Reader's Digest presented as having happened to a teacher at an unnamed community college. Four students walked in halfway through American history test my father was giving at the local community college. "Sorry," they said, "we had a flat tire." An understanding man, Dad said that if they could answer just one question correctly, he would give them each an "A" for the exam. The students agreed. So my father handed each one a piece of paper, placed them in four separate comers and said, "Write down which tire was flat." Kurt Smith What is the probability that these four students would give identical answers if they hadn't had a flat tire? Why?arrow_forward
- A store wants to include cash prizes in bags of potato chips sold at the oldest branch of a popular supermarket. Any bag that is sold, regardless of whether or not it contains a prize, is immediately exchanged for another on the shelf so that the number of bags of chips offered is always the same.The foil pass is maintained with 5 pouches inside at any given time.Each of these bags will have a check with a € 3,000 prize money inside.How many bags should the company make available for sale at one time to make sure that 40% of the time, the first bag of the prize is at least the 5000 that has been sold?arrow_forwardThe 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_forwardIf I go on vacation, I'll spend money. If I spend money, I'll be broke. If I'm broke, I'll have to get another job. What is the conclusion?arrow_forward
- Panaderio 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_forwardYou 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_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