Question 1

The ____________________ of events describes the case where two or more events occur at the same time.

Accepted Answer

intersection

Question 2

Events are ____________________ when the occurrence of one event changes the probability that another will occur.

Accepted Answer

dependent

Question 3

Interest rates
The following represent interest rates on 20 U.S.Treasury bond issues with maturity dates in 2000-2001,as listed in Money Magazine:  
-Using the letter identifications,calculate P (A or F).

Accepted Answer

0.25

Question 4

Probabilities
The prior probabilities for two events AS1U1B11S1U1B0 and AS1U1B12S1U1B0 are P(AS1U1B11S1U1B0)= .30 and P(AS1U1B12S1U1B0)= .70.It is also known that P(AS1U1B11S1U1B0 and AS1U1B12S1U1B0)= 0.Suppose P(B / AS1U1B11S1U1B0)= .15 and P(B / AS1U1B12S1U1B0)= .05.
-Compute P(A2 and B).

Accepted Answer

Question 5

Plan to buy
Intentions of consumers regarding future automobile purchases and the financial capability of the consumers are given below: $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Plan to buy }\
\begin{array} { | c | c c c | } 
\hline \begin{array} { c } 
\text { Qualify for } \
\text { Financing }
\end{array} & \begin{array} { c } 
\text { Within 6 months } \
( \mathrm { A } )
\end{array} & \begin{array} { c } 
\text { 6 months or longer } \
( \mathrm { B } )
\end{array} & \begin{array} { c } 
\text { No } \
\text { (C) }
\end{array} \
\hline \text { Yes (D) } & 0.30 & 0.20 & 0.10 \
\text { No (E) } & 0.10 & 0.10 & 0.20 \
\hline
\end{array}
\end{array}$$
-For a randomly selected consumer,find the following probability: P(A or D).

Accepted Answer

The answer of Plan to buy
Intentions of consumers regarding future...

Question 6

Portfolio Composition
An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds,primarily stocks,or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table:
 $$\begin{array}{l}
\quad \quad \quad \quad \text { Partfolin Compasition }\
\begin{array} { | l | c | c | c | } 
\hline \text { Cender } & \text { Ennds } & \text { Stacks } & \text { Galanced } \
\hline \text { Mala } & 0.18 & 0.20 & 0.25 \
\hline \text { Female } & 0.12 & 0.05 & 0.20 \
\hline
\end{array}
\end{array}$$ One client is selected at random,and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
-Find the following probabilities:
A)P(A or B)
B)P(A and B)

Accepted Answer

The answer of Portfolio Composition
An investment firm has classified its...

Question 7

Dormitory
A dormitory has two activating devices in each fire detector.One is smoke activated and has a probability of .98 of sounding an alarm when it should.The second is a heat sensitive activator and has a probability of .95 of operating when it should.Each activator operates independently of the other.Presume a fire starts near a detector.
-What is the probability that both types of activators will work properly?

Accepted Answer

The answer of Dormitory
A dormitory has two activating devices in...

Question 8

When events are mutually exclusive,two or more of them can happen at the same time.

Accepted Answer

A) True 
 B)False

Question 9

Event 1
The prior probabilities of events AS1U1B11S1U1B0,AS1U1B12S1U1B0,and AS1U1B13S1U1B0 are P(AS1U1B11S1U1B0)= .50,P(AS1U1B12S1U1B0)= .20 and P(AS1U1B13S1U1B0)= .30.The conditional probabilities of event B given AS1U1B11S1U1B0,AS1U1B12S1U1B0,and AS1U1B13S1U1B0 are P(B / AS1U1B11S1U1B0)= .40,P(B / AS1U1B12S1U1B0)= .50 and P(B / AS1U1B13S1U1B0)= .30.
-A state's license plate has 9 positions,each of which has 37 possibilities (26 letters,10 integers,or blank).If the purchaser of a vanity plate wants his first seven positions to be Stanley,in how many ways can his plate appear?

Accepted Answer

The answer of Event 1
The prior probabilities of events AS1U1B11S1U1B0,AS1U1B12S1U1B0,and...

Question 10

Interest rates
The following represent interest rates on 20 U.S.Treasury bond issues with maturity dates in 2000-2001,as listed in Money Magazine:  
-Using the letter identifications,calculate P (B and D).

Accepted Answer

The answer of Interest rates
The following represent interest rates on...

Question 11

Portfolio Composition
An investment firm has classified its clients according to their gender and the composition of their investment portfolio (primarily bonds,primarily stocks,or a balanced mix of bonds and stocks).The proportions of clients falling into the various categories are shown in the following table:
 $$\begin{array}{l}
\quad \quad \quad \quad \text { Partfolin Compasition }\
\begin{array} { | l | c | c | c | } 
\hline \text { Cender } & \text { Ennds } & \text { Stacks } & \text { Galanced } \
\hline \text { Mala } & 0.18 & 0.20 & 0.25 \
\hline \text { Female } & 0.12 & 0.05 & 0.20 \
\hline
\end{array}
\end{array}$$ One client is selected at random,and two events A and B are defined as follows:
A: The client selected is male.
B: The client selected has a balanced portfolio.
-Are A and B independent events? Explain.

Accepted Answer

No; P(A /

Question 12

At a track meet,eight runners are competing in the 100-yard dash.First,second,and third trophies will be awarded.In how many ways can the trophies be awarded?

Accepted Answer

The answer of At a track meet,eight runners are competing...

Question 13

What is the probability that the item is defective?

Accepted Answer

P(D)= P(A)P(D|A)+ P(

Question 14

Candidate
Six candidates for a new position of vice-president for academic affairs have been selected.Three of the candidates are female.The candidates' years of experience are as follows: $$\begin{array} { | c | c | } 
\hline \text { Candidate } & \text { Experience } \
\hline \text { Female 1 } & 5 \
\text { Female 2 } & 9 \
\text { Female 3 } & 11 \
\text { Male 1 } & 6 \
\text { Male 2 } & 4 \
\text { Male 3 } & 8 \
\hline
\end{array}$$ Suppose one of the candidates is selected at random.Define the following events:
A = person selected has 9 years experience.
B = person selected is a female.
Are events A and B independent? Explain using probability.

Accepted Answer

No; P(A/B)

Question 15

Telephone survey
A political telephone survey of 360 people asked whether they were in favor or not in favor of a proposed law.Each person was identified as either Republican or Democrat.The results are shown in the following table:
 $$\begin{array} { | l | c | c | c | c | } 
\hline \text { Party } & \text { In Favar } & \text { Nat in Favar } & \text { Undecided } & \text { Tatal } \
\hline \text { Republican } & 98 & 54 & 4 \square & 192 \
\hline \text { Democrat } & 79 & 29 & 60 & 168 \
\hline \text { Tatal } & 177 & 83 & 100 & 360 \
\hline
\end{array}$$
-What is the probability that a randomly selected respondent was in favor of the proposed law?

Accepted Answer

The answer of Telephone survey
A political telephone survey of 360...

Question 16

Event 1
The prior probabilities of events AS1U1B11S1U1B0,AS1U1B12S1U1B0,and AS1U1B13S1U1B0 are P(AS1U1B11S1U1B0)= .50,P(AS1U1B12S1U1B0)= .20 and P(AS1U1B13S1U1B0)= .30.The conditional probabilities of event B given AS1U1B11S1U1B0,AS1U1B12S1U1B0,and AS1U1B13S1U1B0 are P(B / AS1U1B11S1U1B0)= .40,P(B / AS1U1B12S1U1B0)= .50 and P(B / AS1U1B13S1U1B0)= .30.
-Compute P(B and A3).

Accepted Answer

Question 17

Gulf Coast
A Gulf Coast travel park has the following accommodations:
 $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Number of bedrooms }\
\begin{array} { | l | c | c | c } 
\hline \text { Location } & \text { 3 Gedranm } & \text { 4 Gedranm } & \text { Tatal } \
\hline \text { Beach Frant } & 17 & 24 & 41 \
\hline \text { Nan Beach Frant } & 6 & 210 & 216 \
\hline \text { Tatal } & 23 & 234 & 257 \
\hline
\end{array}
\end{array}$$
-What is the probability of selecting a non beach front site with 3 bedrooms?

Accepted Answer

The answer of Gulf Coast
A Gulf Coast travel park has...

Question 18

Machines
Machine A produces 3% defectives,machine B produces 5% defectives,and machine C produces 10% defectives.Of the total output from these machines,60% of the items are from machine A,30% from B,and 10% from C.One item is selected at random from a day's production.
What is the prior probability that the item came from machine A?
Machine B?
Machine C?

Accepted Answer

P(A)= 0.60

Question 19

Burger Queen Co.
The Burger Queen Company has 124 locations along the west coast.The general manager is concerned with the profitability of the locations compared with major menu items sold.The information below shows the number of each menu item selected by profitability of store. $$\begin{array} { | c | c c c c c | c | } 
\hline \text { Profit } & \begin{array} { c } 
\text { Baby Burger } \
\text { MI }
\end{array} & \begin{array} { c } 
\text { Mother Burger } \
\boldsymbol { M 2 }
\end{array} & \begin{array} { c } 
\text { Father } \
\text { Burger } \boldsymbol { M 3 }
\end{array} & \begin{array} { c } 
\text { Nachos } \
\text { M4 }
\end{array} & \begin{array} { c } 
\text { Tacos } \
\boldsymbol { M S }
\end{array} & \text { Total } \
\hline \text { High Profit } R I & 250 & 424 & 669 & 342 & 284 & 1969 \
\text { Medium Profit } R 2 & 312 & 369 & 428 & 271 & 200 & 1580 \
\text { Low Profit } R 3 & 289 & 242 & 216 & 221 & 238 & 1206 \
\hline \text { Total: } & 851 & 1035 & 1313 & 834 & 722 & 4755 \
\hline
\end{array}$$
-What is the probability of tacos being selected at a low profit store?

Accepted Answer

The answer of Burger Queen Co.
The Burger Queen Company has...

Question 20

From an ordinary deck of 52 playing cards one is selected at random.Define the following events:
A = card selected is an Ace.
B = card selected is a Queen.
C = card selected is a three.
Are A,B,and C mutually exclusive events?
Use the addition rule to find P(A or B or C).

Accepted Answer

The answer of From an ordinary deck of 52 playing...

The ____________________ of events describes the case where two or more events occur at the same time.

Events are ____________________ when the occurrence of one event changes the probability that another will occur.

Interest rates The following represent interest rates on 20 U.S.Treasury bond issues with maturity dates in 2000-2001,as listed in Money Magazine: -Using the letter identifications,calculate P (A or F).

Probabilities The prior probabilities for two events A₁ and A₂ are P(A₁)= .30 and P(A₂)= .70.It is also known that P(A₁ and A₂)= 0.Suppose P(B / A₁)= .15 and P(B / A₂)= .05. -Compute P(A₂ and B).

When events are mutually exclusive,two or more of them can happen at the same time.

Interest rates The following represent interest rates on 20 U.S.Treasury bond issues with maturity dates in 2000-2001,as listed in Money Magazine: -Using the letter identifications,calculate P (B and D).

At a track meet,eight runners are competing in the 100-yard dash.First,second,and third trophies will be awarded.In how many ways can the trophies be awarded?

What is the probability that the item is defective?

Event 1 The prior probabilities of events A₁,A₂,and A₃ are P(A₁)= .50,P(A₂)= .20 and P(A₃)= .30.The conditional probabilities of event B given A₁,A₂,and A₃ are P(B / A₁)= .40,P(B / A₂)= .50 and P(B / A₃)= .30. -Compute P(B and A₃).

Gulf Coast A Gulf Coast travel park has the following accommodations: Number of bedrooms Location 3 Gedranm 4 Gedranm Tatal Beach Frant 17 24 41 Nan Beach Frant 6 210 216 Tatal 23 234 257 -What is the probability of selecting a non beach front site with 3 bedrooms?

From an ordinary deck of 52 playing cards one is selected at random.Define the following events: A = card selected is an Ace. B = card selected is a Queen. C = card selected is a three. Are A,B,and C mutually exclusive events? Use the addition rule to find P(A or B or C).

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Multiple Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

Exam 5: Probability: Review of Basic Concepts

The ____________________ of events describes the case where two or more events occur at the same time.

Events are ____________________ when the occurrence of one event changes the probability that another will occur.

Interest rates The following represent interest rates on 20 U.S.Treasury bond issues with maturity dates in 2000-2001,as listed in Money Magazine: -Using the letter identifications,calculate P (A or F).

Probabilities The prior probabilities for two events A1 and A2 are P(A1)= .30 and P(A2)= .70.It is also known that P(A1 and A2)= 0.Suppose P(B / A1)= .15 and P(B / A2)= .05. -Compute P(A2 and B).

When events are mutually exclusive,two or more of them can happen at the same time.

Interest rates The following represent interest rates on 20 U.S.Treasury bond issues with maturity dates in 2000-2001,as listed in Money Magazine: -Using the letter identifications,calculate P (B and D).

At a track meet,eight runners are competing in the 100-yard dash.First,second,and third trophies will be awarded.In how many ways can the trophies be awarded?

What is the probability that the item is defective?

Event 1 The prior probabilities of events A1,A2,and A3 are P(A1)= .50,P(A2)= .20 and P(A3)= .30.The conditional probabilities of event B given A1,A2,and A3 are P(B / A1)= .40,P(B / A2)= .50 and P(B / A3)= .30. -Compute P(B and A3).

Gulf Coast A Gulf Coast travel park has the following accommodations: Number of bedrooms Location 3 Gedranm 4 Gedranm Tatal Beach Frant 17 24 41 Nan Beach Frant 6 210 216 Tatal 23 234 257 -What is the probability of selecting a non beach front site with 3 bedrooms?

From an ordinary deck of 52 playing cards one is selected at random.Define the following events: A = card selected is an Ace. B = card selected is a Queen. C = card selected is a three. Are A,B,and C mutually exclusive events? Use the addition rule to find P(A or B or C).

A Preview of Business Statistics

Visual Description of Data

Statistical Description of Data

Data Collection and Sampling Methods

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions

Estimation From Sample Data

Hypothesis Tests Involving a Sample Mean or Proportion

Hypothesis Tests Involving Two Sample Means

Analysis of Variance Tests

Chi-Square Applications

Nonparametric Methods

Simple Linear Regression and Correlation

Multiple Regression and Correlation

Model Building

Models for Time Series and Forecasting

Decision Theory

Total Quality Management

Filters

Probabilities The prior probabilities for two events A₁ and A₂ are P(A₁)= .30 and P(A₂)= .70.It is also known that P(A₁ and A₂)= 0.Suppose P(B / A₁)= .15 and P(B / A₂)= .05. -Compute P(A₂ and B).

Event 1 The prior probabilities of events A₁,A₂,and A₃ are P(A₁)= .50,P(A₂)= .20 and P(A₃)= .30.The conditional probabilities of event B given A₁,A₂,and A₃ are P(B / A₁)= .40,P(B / A₂)= .50 and P(B / A₃)= .30. -Compute P(B and A₃).