Question 1

Given P (A)= 0.45, P (B)= 0.30, P (A$\cap$ B)= 0.05.Which of the following is true?

Accepted Answer

A) A and B are independent 
B) A and B are mutually exclusive 
C) A and B are collectively exhaustive 
D) A and B are not independent 
E) A and B are complimentary 
A) A and B are independent 
B) A and B are mutually exclusive 
C) A and B are collectively exhaustive 
D) A and B are not independent 
E) A and B are complimentary D

Question 2

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. $$\begin{array} { | c | c | c | c | c | } 
\hline & \text { A } & \text { B } & \text { C } & \text { Total } \
\hline \text { Under 25 years } & 22 & 34 & 40 & 96 \
\hline 25 \text { or older } & 54 & 28 & 22 & 104 \
\hline \text { Total } & 76 & 62 & 62 & 200 \
\hline
\end{array}$$ If one of these consumers is randomly selected, what is the probability that the person prefers design A?

Accepted Answer

A) 0.76 
B) 0.38 
C) 0.33 
D) 0.22 
E) 0.39 
A) 0.76 
B) 0.38 
C) 0.33 
D) 0.22 
E) 0.39 B

Question 3

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 $$\text { Industry Sector }$
$\begin{array}{|c|c|c|c|c|}
\hline \text { Irvestrnent }\
 \text { Objective } & \text { Electronics } & \text { Airlines } & \text { Healthcare } & \text { Total } \
\hline \text { Growth } & 84 & 21 & 35 & 140 \
\hline \text { Income } & 36 &9& 15 &60 \
\hline \text { Total } & 120 & 30 & 50 & 200\
\hline 
\end{array}$ Which of the following statements is true?

Accepted Answer

A) Growth and Healthcare are complementary events. 
B) Electronics and Growth are independent. 
C) Electronics and Growth are mutually exclusive. 
D) Airlines and Healthcare are collectively exhaustive. 
E) Electronics and Healthcare are collectively exhaustive. 
A) Growth and Healthcare are complementary events. 
B) Electronics and Growth are independent. 
C) Electronics and Growth are mutually exclusive. 
D) Airlines and Healthcare are collectively exhaustive. 
E) Electronics and Healthcare are collectively exhaustive. B

Question 4

An analysis of personal loans at a local bank revealed the following facts: 10% of all personal loans are in default (D), 90% of all personal loans are not in default (D΄), 20% of those in default are homeowners (H | D), and 70% of those not in default are homeowners (H | D΄).If a personal loan is selected at random, P (D | H)= ___________.

Accepted Answer

A) 0.03 
B) 0.63 
C) 0.02 
D) 0.18 
E) 0.78 
A) 0.03 
B) 0.63 
C) 0.02 
D) 0.18 
E) 0.78

Question 5

Given the following joint probability table, find the probability that a dog is small and takes less than 30-minute walks?  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Walk Time }$
$$\begin{array} { | c | c | c | | r | } 
\hline \text { Type of } & & \
 \text { Dog } & < 30 \mathrm {~min} & \geq 30 \mathrm {~min} & \text { Total } \
\hline \text { Bmall } & .29 & .08 & .36 \
\hline \text { Large } & .22 & .41 & .63 \
\hline \text { Total } & .51 & .49 & 1.00 \
\hline
\end{array}$$

Accepted Answer

A) 63% 
B) 22% 
C) 29% 
D) 51% 
E) 32% 
A) 63% 
B) 22% 
C) 29% 
D) 51% 
E) 32%

Question 6

The table below provides summary information about the students in a class.The sex of each individual and their age is given. $$\begin{array} { | l | c | c | c | } 
\hline & \text { Male } & \text { Fernale } & \text { Total } \
\hline \text { Under 20 yrs old } & 10 & 8 & 18 \
\hline \begin{array} { l } 
\text { Between } 20 \text { and } 25 \
\text { yrs old }
\end{array} & 12 & 18 & 30 \
\hline \text { Older tharn 25 yrs. } & 26 & 26 & 52 \
\hline \text { Total } & 48 & 52 & 100 \
\hline
\end{array}$$ A student is randomly selected from this group, and it is found that the student is older than 25 years.What is the probability that the student is a male?

Accepted Answer

A) 0.21 
B) 0.10 
C) 0.50 
D) 0.54 
E) 0.26 
A) 0.21 
B) 0.10 
C) 0.50 
D) 0.54 
E) 0.26

Question 7

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 (Airlines|Income)= _______.

Accepted Answer

A) 0.10 
B) 0.40 
C) 0.25 
D) 0.67 
E) 0.90 
A) 0.10 
B) 0.40 
C) 0.25 
D) 0.67 
E) 0.90

Question 8

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year, P (SUV)= ___________.  $\quad $ $\quad $ $\quad $ $\quad $ $\quad $ $\quad $$\text { Buyer Gender }$
$\begin{array}{|r|c|c||c|}
\hline \text { Type of }\
 \text { Vehicle } & \text { Female } & \text { Male } & \text { Total } \
\hline \text { SUV } & & & \
\hline \text { Not SUV } & .30 & .40 & \
\hline \text { Total } & &.60& 1.00\
\hline
\end{array}$

Accepted Answer

A) 0.30 
B) 0.40 
C) 0.12 
D) 0.10 
E) 0.60 
A) 0.30 
B) 0.40 
C) 0.12 
D) 0.10 
E) 0.60

Question 9

There are three companies that produce a critical electronic navigation component (ENC)used in the aerospace industry.These companies are Alice Manufacturing, Byte International, and Cognizant Technologies.Alice makes 85% of the ENCs, Byte makes 10%, and Cognizant makes the remaining 5%.The ENCs made by Alice have a 2.5% rate of defects, the ones made by Byte have a 4.0% rate of defects, and the ones made by Cognizant have a 6% rate of defects.If an ENC is randomly selected from the general population of ENCs, the probability that it was made by Alice is _______.If this ENC is later tested and found to be defective, the probability that it was made by Alice is _______.

Accepted Answer

A) 0.15; 0.85 
B) 0.85; 0.85 
C) 0.85; 0.77 
D) 0.85; 0.76 
E) 0.85; 0.75 
A) 0.15; 0.85 
B) 0.85; 0.85 
C) 0.85; 0.77 
D) 0.85; 0.76 
E) 0.85; 0.75

Question 10

Max Sandlin researched the characteristics of stock market investors.He found that sixty percent of all investors have a net worth exceeding $1,000,000; 20% of all investors use an online brokerage; and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage.An investor is selected randomly, and E is the event "net worth exceeds $1,000,000" and O is the event "uses an online brokerage." P(O $\cup$ E)= _____________.

Accepted Answer

A) 0.17 
B) 0.50 
C) 0.80 
D) 0.70 
E) 0.10 
A) 0.17 
B) 0.50 
C) 0.80 
D) 0.70 
E) 0.10

Question 11

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

Accepted Answer

A) subjective probability 
B) relative frequency 
C) classical probability 
D) a priori probability 
E) a posterior probability 
A) subjective probability 
B) relative frequency 
C) classical probability 
D) a priori probability 
E) a posterior probability

Question 12

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience, she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.

Accepted Answer

A) subjective probability 
B) relative frequency 
C) classical probability 
D) a priori probability 
E) a posterior probability 
A) subjective probability 
B) relative frequency 
C) classical probability 
D) a priori probability 
E) a posterior probability

Question 13

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Find P (A|B).

Accepted Answer

A) 0.45 
B) 0.135 
C) 0.30 
D) 0.111 
E) 0.167 
A) 0.45 
B) 0.135 
C) 0.30 
D) 0.111 
E) 0.167

Question 14

In the conditional probability of P(E1|E2)is when E2 has occurred and then the probability of E1 occurring is determined.

Accepted Answer

A) True 
 B)False

Question 15

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease.What is the probability of testing positive and having the disease?

Accepted Answer

A) 0.0475 
B) 0.95 
C) 0.05 
D) 0.9 
E) 0.02 
A) 0.0475 
B) 0.95 
C) 0.05 
D) 0.9 
E) 0.02

Question 16

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease and 10% positive reading of people who do not have the disease.What is the probability that a randomly selected person has the disease given that this person is testing positive?

Accepted Answer

A) 0.0475 
B) 0.1425 
C) 0.95 
D) 0.9 
E) 0.3333 
A) 0.0475 
B) 0.1425 
C) 0.95 
D) 0.9 
E) 0.3333

Question 17

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. $$\begin{array} { | r | r | r | r | r | } 
\hline & \text { A } & \text { B } & \text { C } & \text { Total } \
\hline \text { Under 25 years } & 22 & 34 & 40 & 96 \
\hline \text { 25 or older } & 54 & 28 & 22 & 104 \
\hline \text { Total } & 76 & 62 & 62 & 200 \
\hline
\end{array}$$ If one of these consumers is randomly selected and prefers design B, what is the probability that the person is 25 or older?

Accepted Answer

A) 0.28 
B) 0.14 
C) 0.45 
D) 0.27 
E) 0.78 
A) 0.28 
B) 0.14 
C) 0.45 
D) 0.27 
E) 0.78

Question 18

A recently published study shows that 50% of Americans adults take multivitamins regularly.Another recent study showed that 20.6% of American adults work out regularly.Suppose that these two variables are independent.The probability that a randomly selected American adult takes multivitamins regularly and works out regularly is _______.

Accepted Answer

A) 0.706 
B) 0.309 
C) 0.155 
D) 0.106 
E) 0.103 
A) 0.706 
B) 0.309 
C) 0.155 
D) 0.106 
E) 0.103

Question 19

If E and F are mutually exclusive, then _______.

Accepted Answer

A) the probability of the union is zero 
B) P(
E) = 1 - P(F) 
C) the probability of the intersection is zero 
D) the probability of the union is one 
E) P(
E) = P(F) 
A) the probability of the union is zero 
B) P(
E) = 1 - P(F) 
C) the probability of the intersection is zero 
D) the probability of the union is one 
E) P(
E) = P(F)

Question 20

The department in which you work in your company has 24 employees: 10 women and 14 men.A team of 4 employees must be selected to represent the department at a companywide meeting in the headquarters of the company.The team must have two women and two men.How many different teams of 4 can be selected?

Accepted Answer

A) 12 
B) 35 
C) 136 
D) 2024 
E) 4095 
A) 12 
B) 35 
C) 136 
D) 2024 
E) 4095

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Which of the following is true?

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience, she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Find P (A|B).

In the conditional probability of P(E₁|E₂)is when E₂ has occurred and then the probability of E₁ occurring is determined.

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease.What is the probability of testing positive and having the disease?

If E and F are mutually exclusive, then _______.

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

Given P (A)= 0.45, P (B)= 0.30, P (A ∩\cap∩ B)= 0.05.Which of the following is true?

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience, she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.

Given P (A)= 0.45, P (B)= 0.30, P (A ∩\cap∩ B)= 0.05.Find P (A|B).

In the conditional probability of P(E1|E2)is when E2 has occurred and then the probability of E1 occurring is determined.

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease.What is the probability of testing positive and having the disease?

If E and F are mutually exclusive, then _______.

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

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Which of the following is true?

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Find P (A|B).

In the conditional probability of P(E₁|E₂)is when E₂ has occurred and then the probability of E₁ occurring is determined.