Finite Mathematics & Its Applications (12th Edition)
12th Edition
ISBN: 9780134437767
Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 9, Problem 13RE
(a)
To determine
To calculate: The optimal strategies for Ruth and Carol for the game in which they both simultaneously show one of the two cards they have, numbered two and six.
(b)
To determine
To calculate: The player which is favored by the game in which Ruth and Carol both simultaneously show one of the two cards they have, numbered two and six.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
In this game, two chips are placed in a cup. One chip has two red sides
and one chip has a red and a blue side. The player shakes the cup and
dumps out the chips. The player wins if both chips land red side up and
loses if one chip lands red side up and one chip lands blue side up. The
cost to play is $4 and the prize is worth $6. Is this a fair game.
= Win a prize
= Do not win a prize
1. Start by determining the probabilities for winning a prize and not
winning a prize. Draw a probability tree to find the possible outcomes
and the probabilities. After you draw the tree, check you work by
clicking on the link below.
Click to hide hint
CHIP 1
CHIP 2
Probability
P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25
0.5
0.5
0.5
P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25
Start
0.5
0.5
P(Red) & P(Red) = P(R) - P(R) = 0.5. 0.5 = 0.25
0.5
P(Red) & P(Blue) = P(R) - P(B) = 0.5.0.5 = 0.25
A game consists of rolling a colored die with three red sides, two green sides, and one blue side. A roll of red loses. A roll of green pays $2.00. A roll of blue pays $5.00. The charge to play the game is $2.00. Would you play the game? Why or why not?
In this game, two chips are placed in a cup. One chip has two red sides and one chip has a red and a blue side
The player shakes the cup and dumps out the chips. The player wins if both chips land red side up and loses if
one chip lands red side up and one chip lands blue side up. The cost to play is $4 and the prize is worth $6. Is
this a fair game.
= Win a prize
= Do not win a prize
1. Start by determining the probabilities for winning a prize and not winning a prize. Draw a probability tree to
find the possible outcomes and the probabilities. After you draw the tree, check you work by clicking on the link
below.
Click to view hint
2. Create the probability distribution of the game. Fill in the missing parts of the chart.
x → Number of Red Chips
P(x)
Result
1
Lose +
Win +
3. Now find the expected value.
x, Number of red chips X → Net Money Won or Lost
P(x)
1
2$
4. What is the expected Value?
MacBook Air
D00
F3
F4
F5
F7
F8
$
*
4
5
7
8
9
6.
Chapter 9 Solutions
Finite Mathematics & Its Applications (12th Edition)
Ch. 9.1 - Solutions can be found following the section...Ch. 9.1 - Prob. 2CYUCh. 9.1 - Prob. 3CYUCh. 9.1 - Prob. 1ECh. 9.1 - Prob. 2ECh. 9.1 - Prob. 3ECh. 9.1 - Prob. 4ECh. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - Prob. 7E
Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 112, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - In Exercises 1–12, determine the optimal pure...Ch. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - For each of the games that follow, give the payoff...Ch. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.2 - Solutions can be found following the section...Ch. 9.2 - Prob. 2CYUCh. 9.2 - Prob. 1ECh. 9.2 - Suppose that a game has payoff matrix [102120011]...Ch. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Flood Insurance A small business owner must decide...Ch. 9.2 - 7. Two players, Robert and Carol, play a game with...Ch. 9.2 - Rework Exercise 7 with [.7.3] as Roberts strategy.Ch. 9.2 - Two players, Robert and Carol, play a game with...Ch. 9.2 - 10. Rework Exercise 9 with as Robert’s...Ch. 9.2 - 11. Assume that two players, Renée and Carlos,...Ch. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - 16. Three-Finger Morra Reven and Coddy play a game...Ch. 9.3 - Prob. 1CYUCh. 9.3 - Prob. 2CYUCh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - In Exercises 5–12, determine the value of the game...Ch. 9.3 - In Exercises 512, determine the value of the game...Ch. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - In Exercises 13–16, determine the value of the...Ch. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Football Suppose that, when the offense calls a...Ch. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Three-Finger Mor ra Reven and Coddy play a game in...Ch. 9.3 - Advertising Strategies The Carter Company can...Ch. 9 - 1. What do the individual entries of a payoff...Ch. 9 - Prob. 2FCCECh. 9 - Prob. 3FCCECh. 9 - Prob. 4FCCECh. 9 - Prob. 5FCCECh. 9 - Prob. 6FCCECh. 9 - Prob. 7FCCECh. 9 - What is meant by the optimal mixed strategies of R...Ch. 9 - In Exercises 14, state whether or not the games...Ch. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - Prob. 4PCh. 9 - Prob. 5PCh. 9 - Prob. 6P
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- A game involves drawing a single card from a standard deck. The player receives $10 for an ace, $5 for a king, and $1 for a red card that is neither an ace nor a king. Otherwise, the player receives nothing. If the cost of each draw is $2, should you play? Explain your answer mathematically.arrow_forwardZara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game.arrow_forwardZara and Sue play the following game. Each of them roll a fair six-sided die once. If Sue’s number is greater than or equal to Zara’s number, she wins the game. But if Sue rolled a number smaller than Zara’s number, then Zara rolls the die again. If Zara’s second roll gives a number that is less than or equal to Sue’s number, the game ends with a draw. If Zara’s second roll gives a number larger than Sue’s number, Zara wins the game. Find the probability that Zara wins the game and the probability that Sue wins the game. Note: Sue only rolls a die once. The second roll, if the game goes up to that point, is made only by Zara.arrow_forward
- Please answer the question below. SHOW ALL WORK! A bag has 6 red marbles, 3 blue marbles, and 1 orange marble. In a game to raise money for a class trip; parents pay $5 and pull a marble randomly from the bag. The payout is $10 for pulling an orange marble, $4 for a blue marble, and $1 for a red marble. How much can the class expect to earn per game?arrow_forwardPlease answer ASAP Consider the following game played by four individuals, players 1, 2, 3, and 4. Each individual has $10,000. Each player can donate between $0 and $10,000 to build a public park that costs $20,000. If they collect enough money, they construct the park, which is worth $9,000 to each of them. However, if they collect less than $20,000, they cannot build a park. Furthermore, regardless of whether the park is built or not, individuals lose any donations that they make. a) Describe the Nash equilibria for a simultaneous game. What makes them equilibria? Hint: There are many equilibria, so you may want to use a mathematical expression! b) Suppose that players 1, 2, and 3, each donate $4,000 for the park. How much will player 4 donate and why. What are the resulting payoffs for the players? c) Suppose instead that player 1 donated first, player 2 second, player 3 third, and player 4 last. Furthermore, players could only donate in intervals of 1,000 (0, $1,000, $2,000,…arrow_forwardAshleigh and Pavak play a game that begins with a pile of 100 toothpicks. They alternate turns with Ashleigh going first. On each player’s turn, they must remove 1, 3, or 4 toothpicks from the pile. The player who removes the last toothpick wins the game. Determine, with proof, which player has a winning strategy.arrow_forward
- Find the saddle point and solve the game Player B Ba B2 B, В, A, 15 A2 6. Player A -7 4 A3 2.arrow_forwardWhat is the maximum profit of this pure strategy game: 6 4 2 -1 Select one: O a. -1 O b. 6 O c. 4 O d. 2arrow_forwardConsider the following game of ’divide the dollar.’ There is a dollar to be split between two players. Player 1 can make any offer to player 2 in increments of 25 cents; that is, player 1 can make offers of 0 cents, 25 cents, 50 cents, 75 cents, and $1. An offer is the amount of the original dollar that player 1 would like player 2 to have. After player 2 gets an offer, she has the option of either accepting or rejecting the offer. If she accepts, she gets the offered amount and player 1 keeps the remainder. If she rejects, neither player gets anything. Draw the game tree.arrow_forward
- Maria plays the following game: There is a jar containing 2 gold coins, 2 silver coins, and 6 bronze coins. She must select two coins. She gets $2 for each gold coin she selects. She gets $1 for each silver coin she selects. She gets nothing for selecting bronze coins. For example, if she picks one gold and one silver coin, she will get $3 total. If she picks one silver and one bronze coin, she gets $1 total. Let X be her winnings for this game. Fill in the pmf table (leave your answers here as fractions). x 0 1 2 3 4 p(x) Compute the expected value. Write your answer as a decimal (as you would a dollar amount): $ .arrow_forwardJane draws a marble from a box containing 5 red marbles, 3 green marbles, and4 blue marbles. She receives $2 for a red marble and $3 for a green marble that she draws.If she draws a blue marble, she loses $4. Is the game fair? How many dollars should Janepay for a draw in a fair game?arrow_forwardThe inventor of a new game believes that the variable cost for producing the game is $0.95 per unit and the fixed cost are $4,700. The inventor sells each game for $1.99. Let c be the number of games producedarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY
Optimization Problems in Calculus; Author: Professor Dave Explains;https://www.youtube.com/watch?v=q1U6AmIa_uQ;License: Standard YouTube License, CC-BY
Introduction to Optimization; Author: Math with Dr. Claire;https://www.youtube.com/watch?v=YLzgYm2tN8E;License: Standard YouTube License, CC-BY