Question 1

State in your own words the probability concept of independence.

Accepted Answer

The probability of t

Question 2

The table below gives the probabilities of combinations of religion and political parties in a major U.S.city. $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Religion }\
\begin{array} { | l | c c c c | } 
\hline\text { Political parties } & \text { Protestant } ( A ) & \text { Catholic } ( B ) & \text { Jewish } ( C ) & \text { Other } ( D ) \
\hline \text { Democrat } ( E ) & 0.35 & 0.10 & 0.03 & 0.02 \
\text { Republican } ( F ) & 0.27 & 0.09 & 0.02 & 0.01 \
\text { Independent } ( G ) & 0.05 & 0.03 & 0.02 & 0.01 \
\hline
\end{array}
\end{array}$$ 
-Which of the following represents two mutually exclusive events?

Accepted Answer

A)  (A and 
D) . 
B)  (A and 
E) . 
C)  (A and F). 
D)  (A and G). 
E)  All of these are mutually exclusive. 
A)  (A and 
D) . 
B)  (A and 
E) . 
C)  (A and F). 
D)  (A and G). 
E)  All of these are mutually exclusive.

Question 3

Assume that A and B are independent events with P(A)= 0.40 and P(B)= 0.30.The probability that both events will occur simultaneously is:

Accepted Answer

A)  0.10. 
B)  0.12. 
C)  0.70. 
D)  0.75. 
E)  1.0. 
A)  0.10. 
B)  0.12. 
C)  0.70. 
D)  0.75. 
E)  1.0.

Question 4

If a set of events includes all the possible outcomes of an experiment,these events are considered to be:

Accepted Answer

A)  mutually exclusive. 
B)  exhaustive. 
C)  intersecting. 
D)  inclusive. 
E)  None of the above. 
A)  mutually exclusive. 
B)  exhaustive. 
C)  intersecting. 
D)  inclusive. 
E)  None of the above.

Question 5

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.
-Find P(A).

Accepted Answer

The answer of Candidate
Six candidates for a new position of...

Question 6

The union of events describes two or more events occurring at the same time.

Accepted Answer

A) True 
 B)False

Question 7

Manufacturers
A large men's store in a mall purchases suits from four different manufacturers in short,regular,and long.Their current selections are given in the contingency table below: $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \text { Маnufacturers }\
\begin{array} { | c | c c c c | c | } 
\hline \text { Length } & \boldsymbol { H M S } & \boldsymbol { H F } & \boldsymbol { R L } & \boldsymbol { J C } & \text { Total } \
\hline S & 15 & 15 & 35 & 35 & 100 \
R & 60 & 70 & 75 & 70 & 275 \
L & 25 & 35 & 40 & 25 & 125 \
\hline \text { Total: } & 100 & 120 & 150 & 130 & 500 \
\hline
\end{array}
\end{array}$$ Let the abbreviations and letters represent the events.For example Event S = a randomly selected suit is short,event HMS = a randomly selected suit is manufactured by HMS.
-Compute P(HMS / S).

Accepted Answer

The answer of Manufacturers
A large men's store in a mall...

Question 8

When events A and B are independent,then P(A and B)= P(A)+ P(B).

Accepted Answer

A) True 
 B)False

Question 9

Event $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \text { Event }\
\begin{array} { | c | c c c c | c | } 
\hline \text { Event } & \boldsymbol { C 1 } & \mathbf { C 2 } & \mathbf { C 3 } & \mathbf { C 4 } & \text { Total } \
\hline \text { DI } & 75 & 125 & 65 & 35 & 300 \
\text { D2 } & 90 & 105 & 60 & 45 & 300 \
\text { D3 } & 135 & 120 & 75 & 70 & 400 \
\hline \text { Total: } & 300 & 325 & 200 & 150 & 1000 \
\hline
\end{array}
\end{array}$$
-Find P (D1)or P (C1).

Accepted Answer

The answer of Event \[\begin{array}{l}
\quad \quad \quad \quad \quad \quad...

Question 10

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 that an item selected at random is a Mother burger?

Accepted Answer

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

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.
-Express each of the following probabilities in words:
A)P(A/B)
B)P(B/A)

Accepted Answer

The probability that the employee select

Question 12

Manufacturers
A large men's store in a mall purchases suits from four different manufacturers in short,regular,and long.Their current selections are given in the contingency table below: $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \text { Маnufacturers }\
\begin{array} { | c | c c c c | c | } 
\hline \text { Length } & \boldsymbol { H M S } & \boldsymbol { H F } & \boldsymbol { R L } & \boldsymbol { J C } & \text { Total } \
\hline S & 15 & 15 & 35 & 35 & 100 \
R & 60 & 70 & 75 & 70 & 275 \
L & 25 & 35 & 40 & 25 & 125 \
\hline \text { Total: } & 100 & 120 & 150 & 130 & 500 \
\hline
\end{array}
\end{array}$$ Let the abbreviations and letters represent the events.For example Event S = a randomly selected suit is short,event HMS = a randomly selected suit is manufactured by HMS.
-Compute P(S and HMS).

Accepted Answer

The answer of Manufacturers
A large men's store in a mall...

Question 13

The table below gives the probabilities of combinations of religion and political parties in a major U.S.city. $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \text { Religion }\
\begin{array} { | l | c c c c | } 
\hline\text { Political parties } & \text { Protestant } ( A ) & \text { Catholic } ( B ) & \text { Jewish } ( C ) & \text { Other } ( D ) \
\hline \text { Democrat } ( E ) & 0.35 & 0.10 & 0.03 & 0.02 \
\text { Republican } ( F ) & 0.27 & 0.09 & 0.02 & 0.01 \
\text { Independent } ( G ) & 0.05 & 0.03 & 0.02 & 0.01 \
\hline
\end{array}
\end{array}$$ 
-What is the probability that a randomly selected person would be an independent whose religion was neither Protestant nor Catholic?

Accepted Answer

A)  0.05 
B)  0.03 
C)  0.02 
D)  0.01 
A)  0.05 
B)  0.03 
C)  0.02 
D)  0.01

Question 14

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.
-Apply Bayes' theorem to compute P(A2 / B).

Accepted Answer

Question 15

A set of events is ____________________ if it includes all the possible outcomes of an experiment.

Accepted Answer

The answer of A set of events is ____________________ if...

Question 16

Manufacturers
A large men's store in a mall purchases suits from four different manufacturers in short,regular,and long.Their current selections are given in the contingency table below: $$\begin{array}{l}
\quad \quad \quad \quad \quad \quad \quad \text { Маnufacturers }\
\begin{array} { | c | c c c c | c | } 
\hline \text { Length } & \boldsymbol { H M S } & \boldsymbol { H F } & \boldsymbol { R L } & \boldsymbol { J C } & \text { Total } \
\hline S & 15 & 15 & 35 & 35 & 100 \
R & 60 & 70 & 75 & 70 & 275 \
L & 25 & 35 & 40 & 25 & 125 \
\hline \text { Total: } & 100 & 120 & 150 & 130 & 500 \
\hline
\end{array}
\end{array}$$ Let the abbreviations and letters represent the events.For example Event S = a randomly selected suit is short,event HMS = a randomly selected suit is manufactured by HMS.
-Compute P(S).

Accepted Answer

The answer of Manufacturers
A large men's store in a mall...

Question 17

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 mutually exclusive events? Explain.

Accepted Answer

No.Since it's possible to be b

Question 18

Two events A and B are said to be mutually exclusive if:

Accepted Answer

A)  P (A /
B) = 1. 
B)  P (B /
A) =1. 
C)  P (A and 
B) =1. 
D)  P (A and 
B) = 0. 
A)  P (A /
B) = 1. 
B)  P (B /
A) =1. 
C)  P (A and 
B) =1. 
D)  P (A and 
B) = 0.

Question 19

Basketball Team
A basketball team at a university is composed of ten players.The team is made up of players who play either guard,forward,or center position.Four of the ten are guards; four of the ten are forwards; and two of the ten are centers.The numbers of the players are 1,2,3,4,for the guards; 5,6,7,8 for the forwards; and 9 and 10 for the centers.The starting five are numbered 1,3,5,7,and 9.Let a player be selected at random from the ten.Define the following events:
A = player selected has a number from 1 to 8.
B = player selected is a guard.
C = player selected is a forward.
D = player selected is a starter.
E = player selected is a center.
-P(E /D)is equal to:

Accepted Answer

A)  0.80. 
B)  0.40. 
C)  0.50. 
D)  0.20. 
E)  0.10. 
A)  0.80. 
B)  0.40. 
C)  0.50. 
D)  0.20. 
E)  0.10.

Question 20

A student is randomly selected from a class.Event A = the student is a male and Event B = the student is a female.Events A and B are:

Accepted Answer

A)  mutually exclusive. 
B)  exhaustive. 
C)  intersecting. 
D)  dependent. 
E)  both A and B. 
A)  mutually exclusive. 
B)  exhaustive. 
C)  intersecting. 
D)  dependent. 
E)  both A and B.

State in your own words the probability concept of independence.

Assume that A and B are independent events with P(A)= 0.40 and P(B)= 0.30.The probability that both events will occur simultaneously is:

If a set of events includes all the possible outcomes of an experiment,these events are considered to be:

The union of events describes two or more events occurring at the same time.

When events A and B are independent,then P(A and B)= P(A)+ P(B).

Event Event Event Total DI 75 125 65 35 300 D2 90 105 60 45 300 D3 135 120 75 70 400 Total: 300 325 200 150 1000 -Find P (D1)or P (C1).

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. -Apply Bayes' theorem to compute P(A₂ / B).

A set of events is ____________________ if it includes all the possible outcomes of an experiment.

Two events A and B are said to be mutually exclusive if:

A student is randomly selected from a class.Event A = the student is a male and Event B = the student is a female.Events A and B are:

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

State in your own words the probability concept of independence.

Assume that A and B are independent events with P(A)= 0.40 and P(B)= 0.30.The probability that both events will occur simultaneously is:

If a set of events includes all the possible outcomes of an experiment,these events are considered to be:

The union of events describes two or more events occurring at the same time.

When events A and B are independent,then P(A and B)= P(A)+ P(B).

Event Event Event Total DI 75 125 65 35 300 D2 90 105 60 45 300 D3 135 120 75 70 400 Total: 300 325 200 150 1000 -Find P (D1)or P (C1).

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. -Apply Bayes' theorem to compute P(A2 / B).

A set of events is ____________________ if it includes all the possible outcomes of an experiment.

Two events A and B are said to be mutually exclusive if:

A student is randomly selected from a class.Event A = the student is a male and Event B = the student is a female.Events A and B are:

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. -Apply Bayes' theorem to compute P(A₂ / B).