Finite Mathematics & Its Applications (12th Edition)
12th Edition
ISBN: 9780134437767
Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
Publisher: PEARSON
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Chapter 9.1, Problem 18E
To determine
The optimal strategies for Rory and Cara for a game of matching coins. Also, to determine if this is a strictly determined game and its value.
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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
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.
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?
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
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