Question 1

Complete the following theoretical probability distribution table. $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Outcome } & a & b & c & d & e \
\hline \text { Probability } & 0.1 & 0.1 &   & 0.1 & 0.05 \
\hline
\end{array}$$

Accepted Answer

A) 0.65 
B)  0.75 
C)  0.45 
D)  0.64 
E)  0.7 
A) 0.65 
B)  0.75 
C)  0.45 
D)  0.64 
E)  0.7

Question 2

A University of Montana study shows the following one-generation transition probabilities among four major income groups. In the long term, what percentage of male earners would you expect to find in each category  Round your answers to two decimal places. $$\begin{array} { | l | l | l | l | l | } 
\hline  { \begin{array} { l } 
\text { Father's } \
\text { Income }
\end{array} } & { \text { Son's income } } \
 & \begin{array} { l } 
\text { Bottom } \
\mathbf { 1 0 \% }
\end{array} & \mathbf { 1 0 - 5 0 \% } & \mathbf { 5 0 - 9 0 \% } & \begin{array} { l } 
\text { Top } \
\mathbf { 1 0 \% }
\end{array} \
\hline \begin{array} { l } 
\text { Bottom } \
\mathbf { 1 0 \% }
\end{array} & 0.4 & 0.32 & 0.27 & 0.01 \
\hline \mathbf { 1 0 - 5 0 \% } & 0.1 & 0.48 & 0.38 & 0.04 \
\hline \mathbf { 5 0 - 9 0 \% } & 0.04 & 0.38 & 0.48 & 0.1 \
\hline \begin{array} { l } 
\text { Top } \
\mathbf { 1 0 \% }
\end{array} & 0.01 & 0.27 & 0.32 & 0.4 \
\hline
\end{array}$$ ?
Bottom 10%: __________%
10-50%: __________%
50-90%: __________%
Top 10%: __________%
?
50-90%
50-90%

Accepted Answer

9.59; 40.4

Question 3

The following table shows the results of a survey of 390 authors by a (fictitious) publishing company: $$\begin{array} { | l | l | l | l | } 
\hline & \begin{array} { l } 
\text { New } \
\text { Authors }
\end{array} & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 60 & 30 & 90 \
\hline \text { Unsuccessful } & 110 & 190 & 300 \
\hline \text { Total } & 170 & 220 & 390 \
\hline
\end{array}$$ ​
An author is chosen at random.
Compute the estimated probability of the event that the author is unsuccessful.

Accepted Answer

The answer of The following table shows the results of...

Question 4

Two of the mathematics professors at Enormous State are Professor A (known for easy grading) and Professor F (known for tough grading). Last semester, roughly half of Professor F's class consisted of former students of Professor A; these students apparently felt encouraged by their (utterly undeserved) high grades. (Professor F's own former students had fled in droves to Professor A's class to try to shore up their grade point averages.) At the end of the semester, as might have been predicted, all of Professor A's former students wound up with a C- or lower. The rest of the students in the class--former students of Professor F who had decided to "stick it out"-fared better, and three quarters of them earned higher than a C-. After discovering what had befallen them, all the students who earned C- or lower got together and decided to send a delegation to the Department Chair to complain that their grade point averages had been ruined by this callous and heartless beast! The contingent was to consist of 20 representatives selected at random from among them. How many of the 20 would you estimate to have been former students of Professor A  ?

Accepted Answer

A) 4 
B)  17 
C)  15 
D)  10 
E)  16 
A) 4 
B)  17 
C)  15 
D)  10 
E)  16

Question 5

A bag contains 4 red marbles, 3 green ones, 2 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has 2 red ones and 1 of each of the other colors.

Accepted Answer

A)   $\frac { 1 } { 7 }$ 
B)    $\frac { 1 } { 14 }$ 
C)    $\frac { 1 } { 11 }$ 
D)    $\frac { 4 } { 21 }$ 
E)    $\frac { 2 } { 5 }$ 
A)   $\frac { 1 } { 7 }$ 
B)    $\frac { 1 } { 14 }$ 
C)    $\frac { 1 } { 11 }$ 
D)    $\frac { 4 } { 21 }$ 
E)    $\frac { 2 } { 5 }$

Question 6

Professor Frank Nabarro insists that all senior physics majors take his notorious physics aptitude test. The test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 60% of the seniors who do go on to a career in physics still fail the test. Further, 76% of all senior physics majors in fact go on to a career in physics. Assuming that you fail the test, what is the probability that you will not go on to a career in physics  Please, round your answer to two decimal places.

Accepted Answer

A) 0.16 
B)  0.34 
C)  0.71 
D)  0.66 
E)  0.46 
A) 0.16 
B)  0.34 
C)  0.71 
D)  0.66 
E)  0.46

Question 7

Determine whether the given information is consistent with a probability distribution. If not, say why.
​ $P ( A ) = 0.1$ ; $P ( B ) = 0.5$ ; $P ( A \cap B ) = 0.1$

Accepted Answer

Yes. Since @#IMG-DLM& is @#IMG-DLM& both

Question 8

The table shows the results of a survey of 100 authors by a publishing company. Compute the conditional probability: An unsuccessful author is established. $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 26 & 31 \
\hline \text { Unsuccessful } & 14 & 55 & 69 \
\hline \text { Total } & 19 & 81 & 100 \
\hline
\end{array}$$

Accepted Answer

The answer of The table shows the results of a...

Question 9

Two indistinguishable dice are rolled. What is the probability of the event $\{ ( 1,2 ) , ( 4,6 ) , ( 5,6 ) \}$

Accepted Answer

A)  $\frac { 5 } { 9 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 17 } { 216 }$ 
D)  $\frac { 5 } { 36 }$ 
E)  $\frac { 17 } { 36 }$ 
A)  $\frac { 5 } { 9 }$ 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 17 } { 216 }$ 
D)  $\frac { 5 } { 36 }$ 
E)  $\frac { 17 } { 36 }$

Question 10

Concerning Internet use In 1998, 59% of all Caucasians in the U.S., 50% of all African-Americans, 58% of all Hispanics, and 54% of residents not classified into one of these groups used the Internet to search for information. At that time, the U.S. population was 69% Caucasian, 12% African-American, and 13% Hispanic. What percentage of U.S. residents who used the Internet for information search were African-American  Express your answer to the nearest 1%.
 
The answer is __________%

Accepted Answer

The answer of Concerning Internet use In 1998, 59% of...

Question 11

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 1. B: The numbers add to 4. C: At least one of the numbers is 1. D: The numbers do not add to 11. Express the following in symbols.  
"Either numbers add to 11 or the red die shows 1".

Accepted Answer

A)  $D ^ { \prime } \cap A$ 
B)  $D ^ { \prime } \cup A ^ { \prime }$ 
C)  $D \cup A$ 
D)    $D \cup A ^ { \prime }$ 
E)    $D ^ { \prime } \cup A$ 
A)  $D ^ { \prime } \cap A$ 
B)  $D ^ { \prime } \cup A ^ { \prime }$ 
C)  $D \cup A$ 
D)    $D \cup A ^ { \prime }$ 
E)    $D ^ { \prime } \cup A$

Question 12

A bag contains 4 red marbles, 2 green ones, 4 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all red ones. Express your answer as a fraction in the lowest terms.

Accepted Answer

The answer of A bag contains 4 red marbles, 2...

Question 13

The table below shows the frequency of outcomes when two distinguishable coins are tossed 4,000 times and the uppermost faces were observed. What is the estimated probability that the second coin lands with heads up  $$\begin{array} { | l | l | l | l | l | } 
\hline \text { Outcome } & \text { HH } & \text { HT } & \text { TH } & \text { TT } \
\hline \text { Frequency } & 900 & 750 & 1,200 & 1,150 \
\hline
\end{array}$$

Accepted Answer

A) 0.2875 
B)  0.225 
C)  0.475 
D)  0.46 
E)  0.525 
A) 0.2875 
B)  0.225 
C)  0.475 
D)  0.46 
E)  0.525

Question 14

You are given a transition matrix  P. Find the steady-state distribution vector.   $$P = \left[ \begin{array} { l l } 
\frac { 1 } { 5 } & \frac { 4 } { 5 } \
\frac { 1 } { 3 } & \frac { 2 } { 3 }
\end{array} \right]$$

Accepted Answer

A) The steady-state distribution vector is $\left[ \begin{array} { l l } 
\frac { 12 } { 17 } & \frac { 5 } { 17 }
\end{array} \right]$ 
B)  The steady-state distribution vector is $\left[ \begin{array} { l l } 
\frac { 1 } { 2 } & \frac { 1 } { 2 }
\end{array} \right]$ 
C)  The steady-state distribution vector is $\left[ \frac { 3 } { 13 } \frac { 10 } { 13 } \right]$ 
D)  The steady-state distribution vector is $\left[ \frac { 5 } { 17 } \frac { 12 } { 17 } \right]$ 
E)  The steady-state distribution vector is $\left[ \begin{array} { l l } 
\frac { 10 } { 13 } & \frac { 3 } { 13 }
\end{array} \right]$ 
A) The steady-state distribution vector is $\left[ \begin{array} { l l } 
\frac { 12 } { 17 } & \frac { 5 } { 17 }
\end{array} \right]$ 
B)  The steady-state distribution vector is $\left[ \begin{array} { l l } 
\frac { 1 } { 2 } & \frac { 1 } { 2 }
\end{array} \right]$ 
C)  The steady-state distribution vector is $\left[ \frac { 3 } { 13 } \frac { 10 } { 13 } \right]$ 
D)  The steady-state distribution vector is $\left[ \frac { 5 } { 17 } \frac { 12 } { 17 } \right]$ 
E)  The steady-state distribution vector is $\left[ \begin{array} { l l } 
\frac { 10 } { 13 } & \frac { 3 } { 13 }
\end{array} \right]$

Question 15

The phrase "Dogs of the Dow" refers to the stocks listed in the Dow with the highest dividend yield. This table shows the top ten stocks of the "Dogs in the Dow" list. If you selected four of these stocks at random, what is the probability that your selection included the company with the highest yield and excluded the company with the lowest yield  $$\begin{array} { | c | c | c | } 
\hline \text { Symbol } & \text { Company } & \text { Yield } \
\hline \text { SBC } & \begin{array} { c } 
\text { SBC } \
\text { Communications }
\end{array} & 5.48 \% \
\hline \text { GM } & \text { General Motors } & 5.48 \% \
\hline \text { MRK } & \text { Merck } & 5.42 \% \
\hline \text { MO } & \text { Altria } & 4.55 \% \
\hline \text { VZ } & \text { Verizon } & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 3.68 \% \
\hline \text { C } & \text { Citigroup } & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 2.96 \% \
\hline \text { GE } & \text { General Electric } & 2.46 \% \
\hline
\end{array}$$

Accepted Answer

The answer of The phrase "Dogs of the Dow" refers...

Question 16

Professor Frank Nabarro insists that all senior physics majors take his notorious physics aptitude test. The test is so tough that anyone not going on to a career in physics has no hope of passing, whereas 60% of the seniors who do go on to a career in physics still fail the test. Further, 76% of all senior physics majors in fact go on to a career in physics. Assuming that you fail the test, what is the probability that you will not go on to a career in physics  Please, round your answer to two decimal places.
 
The probability is __________.

Accepted Answer

The answer of Professor Frank Nabarro insists that all senior...

Question 17

The following table shows hypothetical U.S. employment figures, broken down by educational attainment. All numbers are in millions and represent civilians aged 16 years and over. Those classed as "Not in Labor Force" were not employed nor actively seeking employment. Find the probability that a person was employed given that the person has more than 4 years of high school. Please round the answer to two decimal places. $$\begin{array} { | l | l | l | l | l | } 
\hline & \text { Employed } & \text { Unemployed } & \begin{array} { l } 
\text { Not in } \
\text { Labor } \
\text { Force }
\end{array} & \text { Total } \
\hline \text { Less Than 4 Years } & 11.1 & 1.1 & 10.4 & 22.6 \
\text { High School } \
\hline \begin{array} { l } 
\text { More than 4 Years } \
\text { High School }
\end{array} & 66.6 & 3.2 & 19.2 & 89 \
\hline \text { Total } & 77.7 & 4.3 & 29.6 & 111.6 \\hline
\end{array}$$

Accepted Answer

A) 0.76 
B)  0.96 
C)  0.97 
D)  0.77 
E)  0.75 
A) 0.76 
B)  0.96 
C)  0.97 
D)  0.77 
E)  0.75

Question 18

This pie-chart shows the ethnic makeup of California schools in the 1981-1982 academic year. What is the probability that a randomly selected California student is neither Hispanic or Latino, nor White 
     
The probability is __________%.

Accepted Answer

The answer of This pie-chart shows the ethnic makeup of...

Question 19

The following table shows the results of a survey of authors by a (fictitious) publishing company: $\begin{array}{|l|l|l|l|}
\hline & \text { New Authors } & \begin{array}{l}
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 25 & 30 \
\hline \text { Unsuccessful } & 15 & 55 & 70 \
\hline \text { Total } & 20 & 80 & 100 \
\hline
\end{array}$  
Consider the following events:
S: An author is successful; U: An author is unsuccessful; N: An author is new; and E: An author is established.
Are the events N and S mutually exclusive

Accepted Answer

The answer of The following table shows the results of...

Question 20

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 11. Express the following in symbols.
​
"Either numbers add to 11 or at least one die shows 2."

Accepted Answer

The answer of Suppose two dice (one green, one red)...

Complete the following theoretical probability distribution table. Outcome a b c d e Probability 0.1 0.1 0.1 0.05

A bag contains 4 red marbles, 3 green ones, 2 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has 2 red ones and 1 of each of the other colors.

Determine whether the given information is consistent with a probability distribution. If not, say why. $P ( A ) = 0.1$ ; $P ( B ) = 0.5$ ; $P ( A \cap B ) = 0.1$

The table shows the results of a survey of 100 authors by a publishing company. Compute the conditional probability: An unsuccessful author is established. New Authors Established Authors Total Successful 5 26 31 Unsuccessful 14 55 69 Total 19 81 100

Two indistinguishable dice are rolled. What is the probability of the event $\{ ( 1,2 ) , ( 4,6 ) , ( 5,6 ) \}$

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 1. B: The numbers add to 4. C: At least one of the numbers is 1. D: The numbers do not add to 11. Express the following in symbols. "Either numbers add to 11 or the red die shows 1".

A bag contains 4 red marbles, 2 green ones, 4 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all red ones. Express your answer as a fraction in the lowest terms.

The table below shows the frequency of outcomes when two distinguishable coins are tossed 4,000 times and the uppermost faces were observed. What is the estimated probability that the second coin lands with heads up Outcome HH HT TH TT Frequency 900 750 1,200 1,150

You are given a transition matrix P. Find the steady-state distribution vector. $P = \left[ \begin{array} { l l } \frac { 1 } { 5 } & \frac { 4 } { 5 } \\\frac { 1 } { 3 } & \frac { 2 } { 3 }\end{array} \right]$

This pie-chart shows the ethnic makeup of California schools in the 1981-1982 academic year. What is the probability that a randomly selected California student is neither Hispanic or Latino, nor White The probability is __________%.

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 11. Express the following in symbols. "Either numbers add to 11 or at least one die shows 2."

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Exam 8: Probability

Complete the following theoretical probability distribution table. Outcome a b c d e Probability 0.1 0.1 0.1 0.05

A bag contains 4 red marbles, 3 green ones, 2 white ones, and 1 purple one. Michelle reaches into the bag and grabs 5 of the marbles. Find the probability that she has 2 red ones and 1 of each of the other colors.

Determine whether the given information is consistent with a probability distribution. If not, say why. ​ P(A)=0.1P ( A ) = 0.1P(A)=0.1 ; P(B)=0.5P ( B ) = 0.5P(B)=0.5 ; P(A∩B)=0.1P ( A \cap B ) = 0.1P(A∩B)=0.1

The table shows the results of a survey of 100 authors by a publishing company. Compute the conditional probability: An unsuccessful author is established. New Authors Established Authors Total Successful 5 26 31 Unsuccessful 14 55 69 Total 19 81 100

Two indistinguishable dice are rolled. What is the probability of the event {(1,2),(4,6),(5,6)}\{ ( 1,2 ) , ( 4,6 ) , ( 5,6 ) \}{(1,2),(4,6),(5,6)}

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 1. B: The numbers add to 4. C: At least one of the numbers is 1. D: The numbers do not add to 11. Express the following in symbols. "Either numbers add to 11 or the red die shows 1".

A bag contains 4 red marbles, 2 green ones, 4 white ones, and 1 purple one. Michelle reaches into the bag and grabs 6 of the marbles. Find the probability that she does not have all red ones. Express your answer as a fraction in the lowest terms.

The table below shows the frequency of outcomes when two distinguishable coins are tossed 4,000 times and the uppermost faces were observed. What is the estimated probability that the second coin lands with heads up Outcome HH HT TH TT Frequency 900 750 1,200 1,150

You are given a transition matrix P. Find the steady-state distribution vector. P=[15451323]P = \left[ \begin{array} { l l } \frac { 1 } { 5 } & \frac { 4 } { 5 } \\\frac { 1 } { 3 } & \frac { 2 } { 3 }\end{array} \right]P=[51​31​​54​32​​]

This pie-chart shows the ethnic makeup of California schools in the 1981-1982 academic year. What is the probability that a randomly selected California student is neither Hispanic or Latino, nor White The probability is __________%.

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 11. Express the following in symbols. ​ "Either numbers add to 11 or at least one die shows 2."

Functions and Applications

Nonlinear Functions and Models

The Mathematics of Finance

Systems of Linear Equations and Matrices

Matrix Algebra and Applications

Linear Programming

Sets and Counting

Random Variables and Statistics

Introduction to the Derivative

Techniques of Differentiation

Applications of the Derivative

The Integral

Further Integration Techniques and Applications of the Integral

Functions of Several Variables

Trigonometric Models

Filters

Determine whether the given information is consistent with a probability distribution. If not, say why. $P ( A ) = 0.1$ ; $P ( B ) = 0.5$ ; $P ( A \cap B ) = 0.1$

Two indistinguishable dice are rolled. What is the probability of the event $\{ ( 1,2 ) , ( 4,6 ) , ( 5,6 ) \}$

You are given a transition matrix P. Find the steady-state distribution vector. $P = \left[ \begin{array} { l l } \frac { 1 } { 5 } & \frac { 4 } { 5 } \\\frac { 1 } { 3 } & \frac { 2 } { 3 }\end{array} \right]$

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 11. Express the following in symbols. "Either numbers add to 11 or at least one die shows 2."