Question 1

If A and B are mutually exclusive, $P ( A ) = 0.2$ , and $P ( B ) = 0.6$ , find $P ( A \cup B ) ^ { \prime }$ .

Accepted Answer

A)  $P ( A \cup B ) ^ { \prime } = 0.2$ 
B)  $P ( A \cup B ) ^ { \prime } = 0.88$ 
C)  $P ( A \cup B ) ^ { \prime } = 0.92$ 
D)  $P ( A \cup B ) ^ { \prime } = 0.12$ 
E)  $P ( A \cup B ) ^ { \prime } = 0.38$ 
A)  $P ( A \cup B ) ^ { \prime } = 0.2$ 
B)  $P ( A \cup B ) ^ { \prime } = 0.88$ 
C)  $P ( A \cup B ) ^ { \prime } = 0.92$ 
D)  $P ( A \cup B ) ^ { \prime } = 0.12$ 
E)  $P ( A \cup B ) ^ { \prime } = 0.38$

Question 2

This table shows the results of a survey of authors by a (fictitious) publishing company $$\begin{array} { | l | l | l | l | } 
\hline & \text { New Authors } & \begin{array} { l } 
\text { Established } \
\text { Authors }
\end{array} & \text { Total } \
\hline \text { Successful } & 5 & 25 & 30 \
\hline \text { Unsuccessful } & 15 & 55 & 70 \
\hline \text { Total } & 20 & 80 & 100 \
\hline
\end{array}$$  
What percentage of established authors are unsuccessful  Express your answer to the nearest hundredth of a percent.
__________%
 
What percentage of unsuccessful authors are established  Express your answer to the nearest hundredth of a percent.
 
__________%

Accepted Answer

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

Question 3

Calculate the estimated probability using the given information. ​
​N​ = 200, fr(E) = 20
​

Accepted Answer

A) 0.27 
B)  ​0.05 
C)  ​0.1 
D)  ​0.9 
E)  ​0.45 
A) 0.27 
B)  ​0.05 
C)  ​0.1 
D)  ​0.9 
E)  ​0.45

Question 4

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 of the Dow" list. If you selected two of these stocks at random, what is the probability that both the stocks in your selection had yields of 4.5% or more  $$\begin{array} { | c | c | c | } 
\hline \text { Symbol } & \text { Company } & \text { Yield } \
\hline \text { SBC } & \text { SBC Communications } & 5.46 \% \
\hline \text { GM } & \text { General Motors } & 5.46 \% \
\hline \text { MRK } & \text { Merck } & 5.42 \% \
\hline \text { MO } & \text { Altria } & 4.55 \% \
\hline \text { VZ } & \text { Verizon } & 4.32 \% \
\hline \text { JPM } & \text { JP Morgan Chase } & 3.78 \% \
\hline \text { C } & \text { Citigroup } & 3.64 \% \
\hline \text { PFE } & \text { Pfizer } & 3.12 \% \
\hline \text { DD } & \text { DuPont } & 2.96 \% \
\hline \text { GE } & \text { General Electric } & 2.46 \% \
\hline
\end{array}$$

Accepted Answer

A)  $\frac { 13 } { 30 }$ 
B)  $\frac { 2 } { 15 }$ 
C)  $\frac { 13 } { 15 }$ 
D)  $\frac { 1 } { 15 }$ 
E)  $\frac { 1 } { 45 }$ 
A)  $\frac { 13 } { 30 }$ 
B)  $\frac { 2 } { 15 }$ 
C)  $\frac { 13 } { 15 }$ 
D)  $\frac { 1 } { 15 }$ 
E)  $\frac { 1 } { 45 }$

Question 5

The following diagram shows the movement of U.S. households among three income groups - affluent, middle class, and poor - over the 11-year period 1978-1989.
   ? $a = 28.8 \%$ , $b = 7.2 \%$ , $c = 30.1 \%$ , $d = 8.3 \%$ ?
Use the transitions shown in the diagram to construct a transition matrix (assuming zero probabilities for the transitions between affluent and poor).
 
Take 1 = Affluent, 2 = Middle class, 3 = Poor.
 
Assuming that the trend shown was to continue, what percent of households classified as affluent in 1978 were predicted to become poor in 2000  (Give your answer to the nearest 0.1%.)
 
The answer is __________%
 
According to the model, what percentage of all U.S. households will be in each income bracket in the long term  (Give your answers to the nearest 0.1 percent.)
 
Percent of affluent is __________%
 
Percent of middle class is __________%
 
Percent of poor is __________%

Accepted Answer

; 2.4; 16.

Question 6

The table shows sales in thousands of units of iPods(R) , Powerbooks(R) and iMac(R) in the fourth quarter of 2001. $$\begin{array} { | l | l | l | l | } 
\hline & \text { iPods } ^ { ( \mathbf { R } ) } & \text { Powerbooks } ^ { ( \mathbf { R } ) } & \text { iMac } ^ { ( \mathbf { R } ) } \
\hline \text { Units } ( \mathbf { 1 } , \mathbf { 0 0 0 } ) & 1,040 & 230 & 240 \
\hline
\end{array}$$ ​
Compute the probability that the item sold in 2001 Q4 was either the PowerBooks(R) or the iMac(R) .
Round to two decimal places, if necessary.
The probability is __________.

Accepted Answer

Question 7

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. ​
A: The red die is 1, 3, or 5; B: The green die is even.
​

Accepted Answer

A) A and B are independent 
B)  A and B are dependent 
A) A and B are independent 
B)  A and B are dependent

Question 8

You are deciding on whether to enroll in Economics 200, Finite Math 300, Greek Poetry 400, or Calculus 500. Describe the event E of avoiding math classes.

Accepted Answer

A)  $E = \{ \text { Finite Math 300, Calculus } 500 \}$ 
B)    $E = \{ \text { Economics 200, Greek Poetry 400, Calculus } 500 \}$ 
C)    $E = \{ \text { Economics 200, Greek Poetry } 400 \}$ 
D)    $E = \{ \text { Greek Poetry } 400 \}$ 
E)    $E = \varnothing$ 
A)  $E = \{ \text { Finite Math 300, Calculus } 500 \}$ 
B)    $E = \{ \text { Economics 200, Greek Poetry 400, Calculus } 500 \}$ 
C)    $E = \{ \text { Economics 200, Greek Poetry } 400 \}$ 
D)    $E = \{ \text { Greek Poetry } 400 \}$ 
E)    $E = \varnothing$

Question 9

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round the answer to four decimal places.  
  $Y _ { 1 }$ , 
  $Y _ { 2 }$ , $Y _ { 3 }$ form a partition of  S.
  $P \left( X \mid Y _ { 1 } \right) = 0.4$ , $P \left( X \mid Y _ { 2 } \right) = 0.5$ , $P \left( X \mid Y _ { 3 } \right) = 0.7$ , $P \left( Y _ { 1 } \right) = 0.7$ , $P \left( Y _ { 2 } \right) = 0.1$ .
 
Find $P \left( Y _ { 1 } \mid X \right)$ .

Accepted Answer

A)  $P \left( Y _ { 1 } \mid X \right) = 0.1064$ 
B)    $P \left( Y _ { 1 } \mid X \right) = 0.5957$ 
C)    $P \left( Y _ { 1 } \mid X \right) = 0.2979$ 
D)    $P \left( Y _ { 1 } \mid X \right) = 0.4043$ 
E)    $P \left( Y _ { 1 } \mid X \right) = 0.098$ 
A)  $P \left( Y _ { 1 } \mid X \right) = 0.1064$ 
B)    $P \left( Y _ { 1 } \mid X \right) = 0.5957$ 
C)    $P \left( Y _ { 1 } \mid X \right) = 0.2979$ 
D)    $P \left( Y _ { 1 } \mid X \right) = 0.4043$ 
E)    $P \left( Y _ { 1 } \mid X \right) = 0.098$

Question 10

It snows in Greenland an average of once in 25 days, and when it does, glaciers have a 15% chance of growing. When it does not snow in Greenland, glaciers have only a 4% chance of growing. What is the probability that it is snowing in Greenland when glaciers are growing  Please, round your answer to four decimal places.
 
The probability is __________.

Accepted Answer

The answer of It snows in Greenland an average of...

Question 11

Tommy the dunker's performance on the basketball court is influenced by his state of mind. If he scores, he is three times as likely to score on the next shot as he is to miss; whereas, if he misses a shot he is four times as likely to miss the next shot as he is to score. In the long term, what percentage of shots are successful

Accepted Answer

A)  $\frac { 4 } { 81 }$ 
B)  $\frac { 5 } { 9 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 4 } { 9 }$ 
E)  $\frac { 6 } { 7 }$ 
A)  $\frac { 4 } { 81 }$ 
B)  $\frac { 5 } { 9 }$ 
C)  $\frac { 2 } { 3 }$ 
D)  $\frac { 4 } { 9 }$ 
E)  $\frac { 6 } { 7 }$

Question 12

You have worked for the Department of Administrative Affairs (DAA) for 27 years, and you still have little or no idea exactly what your job entails. To make your life a little more interesting, you have decided on the following course of action. Every Friday afternoon, you will use your desktop computer to generate a random digit from 0 to 9 (inclusive). If the digit is a eight or greater, you will immediately quit your job, never to return. Otherwise, you will return to work the following Monday. What is the probability that you will still be employed by the DAA after each of the next three weeks  ?

Accepted Answer

A) 0.992 
B)  0.64 
C)  0.512 
D)  1 
E)  0.8 
A) 0.992 
B)  0.64 
C)  0.512 
D)  1 
E)  0.8

Question 13

Find $P \left( A ^ { \prime } \right)$ if $P ( A ) = 0.41$ .

Accepted Answer

A) 0.59 
B)  1.00 
C)  0.41 
D)  0.09 
E)  0.82 
A) 0.59 
B)  1.00 
C)  0.41 
D)  0.09 
E)  0.82

Question 14

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. ​
Find the probability that all 6 are different. Round your answer to four decimal places.
​

Accepted Answer

A) 0.8488 
B)  0.0600 
C)  0.3488 
D)  0.1512 
E)  0.0756 
A) 0.8488 
B)  0.0600 
C)  0.3488 
D)  0.1512 
E)  0.0756

Question 15

Describe the sample space S of the experiment of selecting a letter at random from the word, "Kentucky" and list the elements of the event "choosing a vowel".

Accepted Answer

A)  $S = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ , $E = \{ \mathrm { e } , \mathrm { u } , \mathrm { y } \}$ 
B)  $S = \{ \mathrm { k } , \mathrm { n } , \mathrm { t } , \mathrm { c } , \mathrm { k } \}$ , $E = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ 
C)    $S = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ , $E = \{ \mathrm { a } , \mathrm { e } , \mathrm { i } , \mathrm { o } , \mathrm { y } , \mathrm { u } \}$ 
D)    $S = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ , $E = \{ \mathrm { k } , \mathrm { n } , \mathrm { t } , \mathrm { c } , \mathrm { k } \}$ 
E)    $S = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ , $E = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ 
A)  $S = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ , $E = \{ \mathrm { e } , \mathrm { u } , \mathrm { y } \}$ 
B)  $S = \{ \mathrm { k } , \mathrm { n } , \mathrm { t } , \mathrm { c } , \mathrm { k } \}$ , $E = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ 
C)    $S = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ , $E = \{ \mathrm { a } , \mathrm { e } , \mathrm { i } , \mathrm { o } , \mathrm { y } , \mathrm { u } \}$ 
D)    $S = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ , $E = \{ \mathrm { k } , \mathrm { n } , \mathrm { t } , \mathrm { c } , \mathrm { k } \}$ 
E)    $S = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$ , $E = \{ \mathrm { k } , \mathrm { e } , \mathrm { n } , \mathrm { t } , \mathrm { u } , \mathrm { c } , \mathrm { y } \}$

Question 16

Complete the probability distribution table and then calculate $P ( \{ a , b , e \} )$ . $$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Outcome } & a & b & c & d & e \
\hline \text { Probability } & 0.2 &   & 0.35 & 0.2 & 0.1 \
\hline
\end{array}$$

Accepted Answer

A)  $P ( \{ a , b , e \} ) = 0.55$ 
B)  $P ( \{ a , b , e \} ) = 0.75$ 
C)    $P ( \{ a , b , e \} ) = 0.6$ 
D)  $P ( \{ a , b , e \} ) = 0.45$ 
E)  $P ( \{ a , b , e \} ) = 0.5$ 
A)  $P ( \{ a , b , e \} ) = 0.55$ 
B)  $P ( \{ a , b , e \} ) = 0.75$ 
C)    $P ( \{ a , b , e \} ) = 0.6$ 
D)  $P ( \{ a , b , e \} ) = 0.45$ 
E)  $P ( \{ a , b , e \} ) = 0.5$

Question 17

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. ​
A: Neither die is 4; B: Exactly one die is 3.
​

Accepted Answer

A) A and B are independent 
B)  A and B are dependent 
A) A and B are independent 
B)  A and B are dependent

Question 18

Determine whether the given information is consistent with a probability distribution.   $P ( A ) = 0.7$ ; $P ( B ) = 0$ ; $P ( A \cap B ) = 0$

Accepted Answer

A) Yes 
B)  No 
A) Yes 
B)  No

Question 19

According to a study in The New England Journal of Medicine, 85 of a sample of 5,990 middle-aged men had developed heart disease. It also found that men who were very active (burning about 3,500 calories daily) were half as likely to develop heart disease compared with men who were sedentary. Assume that one-fourth of all middle-aged men are very active, and the rest are classified as sedentary. What is the probability that a middle-aged man with heart disease is very active  Please, round your answer to two decimal places.
?
The probability is __________.

Accepted Answer

The answer of According to a study in The New...

Question 20

A New York Times survey of needy and disabled youths showed that 51% of those who had no preschool education were arrested or charged with a crime by the time they were 19, whereas only 31% who had preschool education wound up in this category. The survey did not specify what percentage of the youths in the survey had preschool education, so let us take a guess at that and estimate that 75% of them had attended preschool. Would youths who had preschool education be more likely to be arrested or charged with a crime than those who did not  ?

Accepted Answer

A) No 
B)  The probabilities are equal 
C)  Yes 
A) No 
B)  The probabilities are equal 
C)  Yes

If A and B are mutually exclusive, $P ( A ) = 0.2$ , and $P ( B ) = 0.6$ , find $P ( A \cup B ) ^ { \prime }$ .

Calculate the estimated probability using the given information. N = 200, fr(E) = 20

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. A: The red die is 1, 3, or 5; B: The green die is even.

You are deciding on whether to enroll in Economics 200, Finite Math 300, Greek Poetry 400, or Calculus 500. Describe the event E of avoiding math classes.

Find $P \left( A ^ { \prime } \right)$ if $P ( A ) = 0.41$ .

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. Find the probability that all 6 are different. Round your answer to four decimal places.

Describe the sample space S of the experiment of selecting a letter at random from the word, "Kentucky" and list the elements of the event "choosing a vowel".

Complete the probability distribution table and then calculate $P ( \{ a , b , e \} )$ . Outcome a b c d e Probability 0.2 0.35 0.2 0.1

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. A: Neither die is 4; B: Exactly one die is 3.

Determine whether the given information is consistent with a probability distribution. $P ( A ) = 0.7$ ; $P ( B ) = 0$ ; $P ( A \cap B ) = 0$

Functions and Applications

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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

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Exam 8: Probability

If A and B are mutually exclusive, P(A)=0.2P ( A ) = 0.2P(A)=0.2 , and P(B)=0.6P ( B ) = 0.6P(B)=0.6 , find P(A∪B)′P ( A \cup B ) ^ { \prime }P(A∪B)′ .

Calculate the estimated probability using the given information. ​ ​N​ = 200, fr(E) = 20 ​

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. ​ A: The red die is 1, 3, or 5; B: The green die is even. ​

You are deciding on whether to enroll in Economics 200, Finite Math 300, Greek Poetry 400, or Calculus 500. Describe the event E of avoiding math classes.

Find P(A′)P \left( A ^ { \prime } \right)P(A′) if P(A)=0.41P ( A ) = 0.41P(A)=0.41 .

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. ​ Find the probability that all 6 are different. Round your answer to four decimal places. ​

Describe the sample space S of the experiment of selecting a letter at random from the word, "Kentucky" and list the elements of the event "choosing a vowel".

Complete the probability distribution table and then calculate P({a,b,e})P ( \{ a , b , e \} )P({a,b,e}) . Outcome a b c d e Probability 0.2 0.35 0.2 0.1

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. ​ A: Neither die is 4; B: Exactly one die is 3. ​

Determine whether the given information is consistent with a probability distribution. P(A)=0.7P ( A ) = 0.7P(A)=0.7 ; P(B)=0P ( B ) = 0P(B)=0 ; P(A∩B)=0P ( A \cap B ) = 0P(A∩B)=0

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

If A and B are mutually exclusive, $P ( A ) = 0.2$ , and $P ( B ) = 0.6$ , find $P ( A \cup B ) ^ { \prime }$ .

Calculate the estimated probability using the given information. N = 200, fr(E) = 20

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. A: The red die is 1, 3, or 5; B: The green die is even.

Find $P \left( A ^ { \prime } \right)$ if $P ( A ) = 0.41$ .

In the New York State daily lottery game, a sequence of 6 (not necessarily different) digits in the range of 0-9 is selected at random. Find the probability that all 6 are different. Round your answer to four decimal places.

Complete the probability distribution table and then calculate $P ( \{ a , b , e \} )$ . Outcome a b c d e Probability 0.2 0.35 0.2 0.1

Two dice (one red and one green) are rolled, and the numbers that face up are observed. Test the pair of events for independence. A: Neither die is 4; B: Exactly one die is 3.

Determine whether the given information is consistent with a probability distribution. $P ( A ) = 0.7$ ; $P ( B ) = 0$ ; $P ( A \cap B ) = 0$