Decision Mathematics 2 Quizzes: Test Your Skills and Prepare for Exams

Question 1

In a zero-sum game, what is the relationship between the payoffs of different players?

Accepted Answer

One player's gain is always another player's loss.

Answer

The total payoffs of all players are always positive.

Answer

There is no Nash equilibrium in a zero-sum game.

Question 2

In a two-player game where neither player can change their strategy once chosen, and both players have only two options (cooperate or defect), what should player A do if player B always cooperates?

Accepted Answer

Always cooperate.

Answer

Always defect.

Answer

Cooperate half of the time.

Question 3

In a linear programming problem, the objective function is the equation that:

Accepted Answer

Represents the total profit or cost

Answer

Defines the feasible region

Answer

Limits the values of the decision variables

Answer

Determines the optimal solution

Question 4

The purpose of the simplex method is to:

Accepted Answer

Find the optimal solution to a linear programming problem

Answer

Solve systems of linear equations

Answer

Find the feasible region of a linear programming problem

Answer

Find the eigenvalues of a matrix

Question 5

A zero-sum game is characterized by:

Accepted Answer

One player's gain is equal to the other player's loss

Answer

The sum of the players' winnings is zero

Answer

Both players can win

Answer

Both players can lose

Question 6

Sensitivity analysis in decision theory helps determine:

Accepted Answer

How changes in input parameters affect the optimal decision

Answer

The most likely outcome of a decision

Answer

The risk associated with a decision

Answer

The optimal objective function

Question 7

Risk aversion in decision theory leads decision-makers to prefer options with:

Accepted Answer

Lower variance

Answer

Higher expected value

Answer

Equal probability of success

Answer

No risk

Question 8

The overarching objective of linear programming is to:

Accepted Answer

Minimize or maximize a linear function subject to constraints

Answer

Find the critical points of a function

Answer

Solve systems of linear equations

Answer

Determine the feasibility of a solution set

Question 9

When we maximize a linear function in linear programming, its dual problem is a:

Accepted Answer

Minimization problem

Answer

Another maximization problem

Answer

Infeasible problem

Answer

Unbounded problem

Question 10

In game theory, a dominant strategy is characterized by being:

Accepted Answer

Always the best choice for a player, regardless of the strategies of other players

Answer

A strategy that leads to a Nash equilibrium

Answer

A strategy that minimizes the loss for a player

Answer

A strategy that guarantees a win for a player

Question 11

The expected value of a decision is calculated as:

Accepted Answer

The sum of the possible outcomes weighted by their probabilities

Answer

The most likely outcome

Answer

The worst possible outcome

Answer

The average of the possible outcomes

Question 12

Sensitivity analysis in linear programming primarily aims to:

Accepted Answer

Determine how changes in input parameters affect the optimal solution

Answer

Identify alternative optimal solutions

Answer

Reduce the number of variables

Answer

Find the feasible region

Question 13

In game theory, a pure strategy involves:

Accepted Answer

Always choosing the same action

Answer

Randomly choosing an action

Answer

Choosing an action based on the strategies of other players

Answer

Choosing the action with the highest expected payoff

Question 14

The optimal solution to the linear programming problem:
Maximize 3x + 2y
Subject to:
x + y ≤ 4
x ≥ 2
y ≥ 1 is:

Accepted Answer

(2, 2)

Answer

(3, 1)

Answer

(4, 0)

Answer

(1, 3)

Question 15

The key distinction between a zero-sum game and a non-zero-sum game is that in a zero-sum game:

Accepted Answer

The gains of one player are offset by the losses of other players, whereas in a non-zero-sum game, this is not the case.

Answer

There is only one winner and one loser, while in a non-zero-sum game, there can be multiple winners or losers.

Answer

The strategies of the players are independent, whereas in a non-zero-sum game, they are interdependent.

Answer

There is no difference between the two types of games.

Question 16

What is the role of Bayes' Theorem in decision theory?

Accepted Answer

To calculate the probability of an event based on conditional probabilities

Answer

To determine the expected value of a decision

Question 17

How are probability and utility related in decision theory?

Accepted Answer

Probability is used to weight the outcomes of different decisions, while utility is used to determine the subjective value of different outcomes.

Answer

Utility is used to determine the subjective value of different outcomes.

Question 18

What is an advantage of using linear programming models in decision-making?

Accepted Answer

They can handle complex problems with multiple variables and constraints.

Answer

They always provide the optimal solution to a problem.

Question 19

Which of the following probability distributions is symmetric about its mean?

Accepted Answer

Normal distribution

Answer

Binomial distribution

Answer

Exponential distribution

Answer

Poisson distribution

Question 20

Which of the following is a key assumption of linear programming?

Accepted Answer

The objective function and constraints must be linear

Answer

The decision variables must be integers

Answer

The solution space must be concave

Answer

The optimal solution always exists

Question 21

Which of the following is NOT a type of sensitivity analysis used in decision-making?

Accepted Answer

Regression analysis

Answer

Scenario analysis

Answer

One-way sensitivity analysis

Answer

Tornado diagram

Question 22

Which of the following is the property of a probability distribution that ensures that the sum of probabilities across all possible outcomes is equal to 1?

Accepted Answer

Normalization

Answer

Independence

Answer

Additivity

Answer

Mutually exclusive

Question 23

Which decision criterion maximizes the expected outcome?

Accepted Answer

Expected Value

Answer

Minimax

Answer

Maximin

Answer

Hurwicz Criterion

Question 24

What is the purpose of introducing slack variables in a linear programming problem?

Accepted Answer

To convert inequalities into equalities

Answer

To minimize the objective function

Answer

To represent constraints graphically

Answer

To determine the optimal solution

Question 25

In a non-zero-sum game, the total outcome for all players can be:

Accepted Answer

Positive or negative, not necessarily zero

Answer

Always a positive value

Answer

Always a negative value

Answer

Always zero

Question 26

What is the purpose of sensitivity analysis in decision-making?

Accepted Answer

To assess how changes in input variables impact the solution

Answer

To predict the future

Answer

To eliminate uncertainty

Answer

To optimize the model

Question 27

Which of the following is NOT a concept in matrix methods?

Accepted Answer

Integration

Answer

Eigenvalues and eigenvectors

Answer

Gaussian elimination

Answer

Linear independence

Question 28

What is the objective of linear programming?

Accepted Answer

To optimize a linear function while satisfying constraints

Answer

To solve a system of linear equations

Answer

To find the shortest path in a network

Answer

To predict future events

Question 29

In a two-player, zero-sum game, if Player A has a dominant strategy, what should Player B do to minimize their potential losses?

Accepted Answer

Play the strategy that minimizes their potential losses against Player A's dominant strategy

Answer

Play a random strategy

Answer

Play a strategy that maximizes their potential gains

Question 30

Which of the following is not a core topic covered in Decision Mathematics 2?

Accepted Answer

Calculus

Answer

Linear programming

Answer

Matrix methods

Answer

Game theory

Question 31

In a zero-sum game, the total payoff to all players always equals:

Accepted Answer

Zero

Answer

A positive value

Answer

A negative value

Answer

An indeterminate value

Question 32

A rational decision-maker should:

Accepted Answer

Choose the alternative that maximizes their expected utility

Answer

Always choose the alternative with the lowest risk

Answer

Consider only their own interests

Answer

Make decisions based on random chance

Question 33

In a zero-sum game, if one player's payoff increases, what happens to the other player's payoff?

Accepted Answer

It decreases.

Answer

It also increases.

Answer

It stays the same.

Answer

It changes randomly.

Question 34

In a two-player, non-zero-sum game, what is a possible outcome for the players?

Accepted Answer

Both players can benefit or lose, depending on their strategies.

Answer

Both players always benefit.

Answer

One player's gain always results in the other player's loss.

Answer

There is always a single best strategy for both players.

Question 35

The objective function of a linear programming model aims to:

Accepted Answer

Maximize a linear function subject to constraints

Answer

Minimize a linear function subject to constraints

Answer

Find the optimal solution to a set of equations

Answer

Determine the feasibility of a given set of constraints

Question 36

In game theory, a Nash equilibrium occurs when:

Accepted Answer

Each player's strategy is their best response to the strategies of the other players, regardless of their own payoffs

Answer

The sum of all players' payoffs is at a maximum

Answer

The game is cooperative and all players agree to a certain strategy

Answer

The winning player has the highest individual payoff

Question 37

Which of the following is NOT a type of decision-making under uncertainty?

Accepted Answer

Linear regression

Answer

Expected value

Answer

Maximax

Answer

Minimax

Question 38

Which of the following is an example of a probabilistic constraint in a linear programming model?

Accepted Answer

x + y ≥ 5 with probability 0.8

Answer

2x - y ≤ 3 with certainty

Answer

x^2 + y^2 ≤ 10 with probability 0.5

Answer

5x + 3y = 15 with probability 1

Question 39

In a game theory scenario, a dominant strategy is one that:

Accepted Answer

Maximizes the player's payoff regardless of the strategies of other players

Answer

Minimizes the player's payoff regardless of the strategies of other players

Answer

Results in a Nash equilibrium if all players adopt it

Answer

Guarantees a win for the player

Question 40

The expected value of a decision is calculated by:

Accepted Answer

Multiplying each possible outcome by its probability and summing the results

Answer

Subtracting the minimum possible outcome from the maximum possible outcome

Answer

Dividing the sum of all possible outcomes by the number of outcomes

Answer

Squaring the probability of the most likely outcome

Question 41

In game theory, which of the following is a pure strategy Nash equilibrium?

Accepted Answer

Player A chooses strategy 1 and Player B chooses strategy 2

Answer

Player A chooses strategy 1 with probability 0.5 and Player B chooses strategy 2 with probability 0.5

Answer

Player A chooses between strategies 1 and 2 randomly, and Player B chooses between strategies 2 and 3 randomly

Answer

Player A chooses strategy 1 and Player B chooses the strategy that minimizes her loss

Question 42

What is the expected value of a fair coin toss?

Accepted Answer

0.5

Answer

0

Answer

1

Answer

2

Question 43

What is the maximum value of the objective function z = 2x + 3y subject to the constraints x + y ≤ 5, x ≥ 0, y ≥ 0?

Accepted Answer

15

Answer

5

Answer

10

Answer

20

Question 44

The adjoint of a matrix A is denoted as:

Accepted Answer

adj(A)

Answer

A^-1

Answer

A^T

Answer

det(A)

Question 45

In a non-zero-sum game, how can the gains and losses of different players be related?

Accepted Answer

The gains of one player can be greater than, equal to, or less than the total losses of all other players.

Answer

The gains of one player are always equal to the total losses of all other players.

Answer

The gains of one player are always less than the total losses of all other players.

Answer

The gains and losses of different players are always unrelated.

Question 46

Maximize Z = 2x + 3y
Subject to:
x + y ≤ 4
2x + y ≤ 6
x ≥ 0, y ≥ 0
Solve the linear programming problem using the graphical method.

Accepted Answer

x = 2, y = 2; Z = 8

Answer

x = 1, y = 3; Z = 7

Answer

x = 0, y = 4; Z = 6

Answer

x = 3, y = 1; Z = 9

Question 47

Which of the following matrices has an inverse?
A matrix with:

Accepted Answer

A non-zero determinant

Answer

More rows than columns

Answer

A row of zeros

Answer

A column of zeros

Question 48

In game theory, what is the value of a zero-sum game?

Accepted Answer

Zero

Answer

Infinite

Answer

Negative

Answer

Positive

Question 49

In linear programming, why are slack variables introduced?

Accepted Answer

To convert inequalities into equations

Answer

To increase the number of variables

Answer

To decrease the number of constraints

Answer

To maximize the objective function

Question 50

Which of the following is a limitation of using matrix methods to solve systems of linear equations?

Accepted Answer

They become computationally intensive for large systems

Answer

They require all coefficients to be non-zero

Answer

They can only solve systems with a unique solution

Question 51

In linear programming, what is the geometric representation of a feasible region?

Accepted Answer

A polyhedron

Answer

A hyperplane

Answer

A circle

Answer

A parabola

Question 52

What is a key difference between linear programming and matrix methods?

Accepted Answer

Linear programming involves optimizing an objective function

Answer

Linear programming requires all variables to be continuous

Answer

Matrix methods can solve systems of any size

Question 53

Which of the following ensures that a square matrix is invertible?

Accepted Answer

Determinant is non-zero

Answer

A is symmetric

Answer

A is diagonalizable

Answer

A has linearly independent rows

Question 54

In a zero-sum game, the sum of the players' payoffs under any strategy profile is:

Accepted Answer

Zero

Answer

Always positive

Answer

Dependent on the strategies chosen

Answer

Always negative

Question 55

An appropriate objective function for a minimization problem is:

Accepted Answer

Minimize z

Answer

Solve for z

Answer

Maximize z

Answer

Equalize z to a constant

Question 56

In a game of perfect information, both players know:

Accepted Answer

All previous moves and payoffs

Answer

Nothing about the other player's strategy

Answer

Only their own moves

Answer

Only the other player's last move

Question 57

Which of these is an assumption of the expected value principle?

Accepted Answer

All possible outcomes and their probabilities are known

Answer

The payoffs are in monetary units

Answer

The decision is made under time pressure

Answer

The decision-maker is risk-averse

Question 58

In a maximization linear programming problem, the optimal solution must occur at:

Accepted Answer

A corner point of the feasible region

Answer

An edge of the feasible region

Answer

An interior point of the feasible region

Answer

Any point on the objective function line

Question 59

In game theory, a saddle point is:

Accepted Answer

A strategy combination where neither player can improve their outcome by unilaterally changing their strategy while the other player's strategy remains unchanged.

Answer

A strategy that guarantees a win for both players

Answer

A strategy that guarantees a loss for both players

Question 60

Which of the following is a key assumption of expected utility theory?

Accepted Answer

Individuals are rational decision-makers who seek to maximize their expected utility

Answer

Individuals are always risk-averse

Answer

The value of an outcome is constant

Answer

The probability of an outcome is known with certainty

Question 61

In a zero-sum game, the sum of the payoffs to all players is:

Accepted Answer

Always zero

Answer

Positive

Answer

Uncertain

Answer

Negative

Question 62

The expected value of a random variable is:

Accepted Answer

The weighted average of all possible outcomes, where the weights are the probabilities of each outcome.

Answer

The average of all possible outcomes

Answer

The most likely outcome

Question 63

A decision tree can be used to:

Accepted Answer

Graphically represent a sequence of decisions and their consequences, allowing for an evaluation of potential outcomes.

Answer

Solve linear equations

Answer

Calculate the probability of events

Question 64

In the linear programming problem: minimize 2x + 3y subject to the constraints x + y >= 4, x - y <= 2, x >= 0, y >= 0, what is the objective function?

Accepted Answer

2x + 3y

Answer

x >= 0

Answer

x + y >= 4

Answer

x - y <= 2