Question 1

If two events are mutually exclusive, then the two events are also independent.

Accepted Answer

A) True 
 B)False

Question 2

Bayes' rule is an extension of the law of conditional probabilities to allow revision of original probabilities with new information.

Accepted Answer

A) True 
 B)False

Question 3

A recent survey found that 24% of people in Michigan like oatmeal.If the probability that someone lives in Michigan is 4.8%.What is the probability that you choose two people in the US and they are both from Michigan?

Accepted Answer

A) 28.4% 
B) 24.0% 
C) 0.2% 
D) 100.0% 
E) 48.0% 
A) 28.4% 
B) 24.0% 
C) 0.2% 
D) 100.0% 
E) 48.0%

Question 4

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.'  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Industry Sector }$
$$\begin{array} { | c | c | c | c | c | } 
\hline \text { Irvestment } & & \
 \text { Objective } & \text { Electronics } & \text { Airlines } & \text { Healthcare } & \text { Total } \
\hline \text { Growth } & 100 & 10 & 40 & 150 \
\hline \text { Income } & 20 & 20 & 10 & 50 \
\hline \text { Total } & 120 & 30 & 50 & 200 \
\hline
\end{array}$$ If a stock is selected randomly from Meagan's portfolio, P (Healthcare $\cap$ Electronics)= _______.

Accepted Answer

A) 0.25 
B) 0.85 
C) 0.60 
D) 0.75 
E) 0.90 
A) 0.25 
B) 0.85 
C) 0.60 
D) 0.75 
E) 0.90

Question 5

Suppose that the probability that LIBOR (London inter-bank offered rate)will increase next trimester is 0.025.Assume also that the probability that your company will open a new branch overseas is 0.20.If the probability that at least one of the two events occur, i.e., LIBOR increases and/or your company opens a new overseas branch, is 0.21, what is the probability that both events occur?

Accepted Answer

A) 0.225 
B) 0.015 
C) 0.010 
D) 0.007 
E) 0.005 
A) 0.225 
B) 0.015 
C) 0.010 
D) 0.007 
E) 0.005

Question 6

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.The complement of F is ___________.

Accepted Answer

A) {Albert, Betty, Jack, Patty} 
B) {Betty, Patty, Meagan} 
C) {Albert, Abel, Jack} 
D) {Betty, Abel} 
E) {Meagan} 
A) {Albert, Betty, Jack, Patty} 
B) {Betty, Patty, Meagan} 
C) {Albert, Abel, Jack} 
D) {Betty, Abel} 
E) {Meagan}

Question 7

The probability that a person's favorite color is blue would be an example of a marginal probability.

Accepted Answer

A) True 
 B)False

Question 8

Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.A student is randomly selected, and it is found that the student is enrolled in finance.What is the probability that this student is also enrolled in statistics?

Accepted Answer

A) 0.15 
B) 0.75 
C) 0.375 
D) 0.50 
E) 0.80 
A) 0.15 
B) 0.75 
C) 0.375 
D) 0.50 
E) 0.80

Question 9

If P(X|Y)= P(X)then the events are X and Y are independent.

Accepted Answer

A) True 
 B)False

Question 10

Your company provides services to three different industries: automotive, construction, and financial services.These services can be either on a yearly or on a monthly contract.The cross-tabulation below summarizes this information: $$\begin{array} { | l | l | l | l | } 
\hline & \text { Morthly } & \text { Yearly } & \text { Total } \
\hline \text { Automotive } & 125 & 85 & 210 \
\hline \text { Construction } & 212 & 351 & 563 \
\hline \text { Finaricial } & 357 & 210 & 567 \
\hline \text { Total } & 694 & 646 & 1340 \
\hline
\end{array}$$ If a client is randomly selected, what is the likelihood that it will be from the financial industry or on a monthly contract?

Accepted Answer

A) 26.6% 
B) 42.3% 
C) 51.8% 
D) 65.5% 
E) 67.5% 
A) 26.6% 
B) 42.3% 
C) 51.8% 
D) 65.5% 
E) 67.5%

Question 11

The method of assigning probabilities to uncertain outcomes based on laws and rules is called the relative frequency method.

Accepted Answer

A) True 
 B)False

Question 12

The list of all elementary events for an experiment is called the sample space.

Accepted Answer

A) True 
 B)False

Question 13

The probability of A $\cup$ B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.

Accepted Answer

A) True 
 B)False

Question 14

In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G).A quality control inspector randomly selects three of the twenty-five castings without replacement, to test.The sample space for selecting the group to test contains ____________ elementary events.

Accepted Answer

A) 12,650 
B) 2,300 
C) 455 
D) 16 
E) 15,625 
A) 12,650 
B) 2,300 
C) 455 
D) 16 
E) 15,625

Question 15

The CEO of Apple wanted to know the probability that someone would own an Apple computer or spend more than 20 hours each week on the internet, this would be an example of a ______________ probability.

Accepted Answer

A) union 
B) unconditional 
C) marginal 
D) conditional 
E) joint 
A) union 
B) unconditional 
C) marginal 
D) conditional 
E) joint

Question 16

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labeled A, B, and C.The consumers are classified according to age and package design preference. $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { A } & \text { B } & \text { C } & \text { Total } \
\hline \text { Under 25 years } & 22 & 34 & 40 & 96 \
\hline 25 \text { or older } & 54 & 28 & 22 & 104 \
\hline \text { Total } & 76 & 62 & 62 & 200 \
\hline
\end{array}$$ Are "B" and "25 or older" independent and why or why not?

Accepted Answer

A) No, because P (25 or over | 
B) $\neq$ P (
B)  
B) Yes, because P (
B) = P(
C)  
C) No, because P (25 or older | 
B) $\neq$ P (25 or older) 
D) Yes, because P (25 or older $\cap$ 
B) $\neq$ 0 
E) No, because age and package design are different things 
A) No, because P (25 or over | 
B) $\neq$ P (
B)  
B) Yes, because P (
B) = P(
C)  
C) No, because P (25 or older | 
B) $\neq$ P (25 or older) 
D) Yes, because P (25 or older $\cap$ 
B) $\neq$ 0 
E) No, because age and package design are different things

Question 17

Bayes' rule is a rule to assign probabilities under the relative frequency method.

Accepted Answer

A) True 
 B)False

Question 18

If two events are mutually exclusive, then their joint probability is always zero.

Accepted Answer

A) True 
 B)False

Question 19

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.'  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Industry Sector }$
$$\begin{array} { | c | c | c | c | c | } 
\hline \text { Irvestment } & & \
 \text { Objective } & \text { Electronics } & \text { Airlines } & \text { Healthcare } & \text { Total } \
\hline \text { Growth } & 100 & 10 & 40 & 150 \
\hline \text { Income } & 20 & 20 & 10 & 50 \
\hline \text { Total } & 120 & 30 & 50 & 200 \
\hline
\end{array}$$ If a stock is selected randomly from Meagan's portfolio, P (Growth)= _______.

Accepted Answer

A) 0.50 
B) 0.83 
C) 0.67 
D) 0.75 
E) 0.90 
A) 0.50 
B) 0.83 
C) 0.67 
D) 0.75 
E) 0.90

Question 20

It is known that 20% of all students in some large university are overweight, 20% exercise regularly and 2% are overweight and exercise regularly.What is the probability that a randomly selected student is either overweight or exercises regularly or both?

Accepted Answer

A) 0.40 
B) 0.38 
C) 0.20 
D) 0.42 
E) 0.10 
A) 0.40 
B) 0.38 
C) 0.20 
D) 0.42 
E) 0.10

If two events are mutually exclusive, then the two events are also independent.

Bayes' rule is an extension of the law of conditional probabilities to allow revision of original probabilities with new information.

A recent survey found that 24% of people in Michigan like oatmeal.If the probability that someone lives in Michigan is 4.8%.What is the probability that you choose two people in the US and they are both from Michigan?

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.The complement of F is ___________.

The probability that a person's favorite color is blue would be an example of a marginal probability.

If P(X|Y)= P(X)then the events are X and Y are independent.

The method of assigning probabilities to uncertain outcomes based on laws and rules is called the relative frequency method.

The list of all elementary events for an experiment is called the sample space.

The probability of A $\cup$ B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.

The CEO of Apple wanted to know the probability that someone would own an Apple computer or spend more than 20 hours each week on the internet, this would be an example of a ______________ probability.

Bayes' rule is a rule to assign probabilities under the relative frequency method.

If two events are mutually exclusive, then their joint probability is always zero.

It is known that 20% of all students in some large university are overweight, 20% exercise regularly and 2% are overweight and exercise regularly.What is the probability that a randomly selected student is either overweight or exercises regularly or both?

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Analysis of Variance and Design of Experiments

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Building Multiple Regression Models

Time-Series Forecasting and Index Numbers

Analysis of Categorical Data

Nonparametric Statistics

Statistical Quality Control

Decision Analysis

Filters

Exam 4: Probability

If two events are mutually exclusive, then the two events are also independent.

Bayes' rule is an extension of the law of conditional probabilities to allow revision of original probabilities with new information.

A recent survey found that 24% of people in Michigan like oatmeal.If the probability that someone lives in Michigan is 4.8%.What is the probability that you choose two people in the US and they are both from Michigan?

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.The complement of F is ___________.

The probability that a person's favorite color is blue would be an example of a marginal probability.

If P(X|Y)= P(X)then the events are X and Y are independent.

The method of assigning probabilities to uncertain outcomes based on laws and rules is called the relative frequency method.

The list of all elementary events for an experiment is called the sample space.

The probability of A ∪\cup∪ B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.

The CEO of Apple wanted to know the probability that someone would own an Apple computer or spend more than 20 hours each week on the internet, this would be an example of a ______________ probability.

Bayes' rule is a rule to assign probabilities under the relative frequency method.

If two events are mutually exclusive, then their joint probability is always zero.

It is known that 20% of all students in some large university are overweight, 20% exercise regularly and 2% are overweight and exercise regularly.What is the probability that a randomly selected student is either overweight or exercises regularly or both?

Introduction to Statistics and Business Analytics

Visualizing Data With Charts and Graphs

Descriptive Statistics

Discrete Distributions

Continuous Distributions

Sampling and Sampling Distributions

Statistical Inference: Estimation for Single Populations

Statistical Inference: Hypothesis Testing for Single Populations

Statistical Inferences About Two Populations

Analysis of Variance and Design of Experiments

Simple Regression Analysis and Correlation

Multiple Regression Analysis

Building Multiple Regression Models

Time-Series Forecasting and Index Numbers

Analysis of Categorical Data

Nonparametric Statistics

Statistical Quality Control

Decision Analysis

Filters

The probability of A $\cup$ B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.