Question 1

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.87$

Accepted Answer

A) 0.87 
B) 0.13 
C) 0.065 
D) 0 
E) 1 
A) 0.87 
B) 0.13 
C) 0.065 
D) 0 
E) 1

Question 2

In order to be certified,an EMT trainee (EMT stands for "emergency medical technician")must pass a written examination.A study of 76 trainees is conducted to assess the effectiveness of exam-preparation seminars in reducing the failure rate.The data are summarized below.$$\begin{array} { | l | l | l | l | l | } 
\hline & 0 \text { seminars attended } & 1 \text { seminar attended } & 2 \text { seminars attended } & \text { Total } \
\hline \text { Passed exam } & 5 & 14 & 19 & 38 \
\hline \text { Failed exam } & 8 & 15 & 15 & 38 \
\hline \text { Total } & 13 & 29 & 34 & 76 \
\hline
\end{array}$$
Find the probability that the trainee attended one seminar and passed the exam.

Accepted Answer

A)  $\frac { 14 } { 29 }$ 
B)  $\frac { 7 } { 19 }$ 
C)  $\frac { 29 } { 76 }$ 
D)  $\frac { 7 } { 38 }$ 
E)  $\frac { 14 } { 47 }$ 
A)  $\frac { 14 } { 29 }$ 
B)  $\frac { 7 } { 19 }$ 
C)  $\frac { 29 } { 76 }$ 
D)  $\frac { 7 } { 38 }$ 
E)  $\frac { 14 } { 47 }$

Question 3

A study of the effectiveness of a flu vaccine was conducted with a sample of 497 people.Some participants in the study were given no vaccine,some were given one injection,and some were given two injections.The results of the study are listed in the table. $$\begin{array} { | l | l | l | l | l | } 
\hline & \text { No vaccine } & \text { One injection } & \text { Two injections } & \text { Total } \
\hline \text { Flu } & 8 & 3 & 12 & 23 \
\hline \text { No flu } & 145 & 52 & 277 & 474 \
\hline \text { Total } & 153 & 55 & 289 & 497 \
\hline
\end{array}$$
A person is selected at random from the sample.Find the specified probability that the person got the flu and had one injection.Round your anser to one decimal place.

Accepted Answer

A) 5.6% 
B) 2.6% 
C) 3.6% 
D) 0.6% 
E) 6.6% 
A) 5.6% 
B) 2.6% 
C) 3.6% 
D) 0.6% 
E) 6.6%

Question 4

You are given the probability that an event will happen.Find the probability that the event will not happen.​ $$P ( E ) = 0.78$$ ​

Accepted Answer

A) 0.37 
B) 0.22 
C) 0.78 
D) 0.27 
E) 0.32 
A) 0.37 
B) 0.22 
C) 0.78 
D) 0.27 
E) 0.32

Question 5

There were approximately 6.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.Estimate the number of unemployed workers in the 16-19 age group.(Round your answer to two decimal places. )​   ​

Accepted Answer

A) 2.97 million 
B) 4.97 million 
C) 1.97 million 
D) 0.97 million 
E) 3.97 million 
A) 2.97 million 
B) 4.97 million 
C) 1.97 million 
D) 0.97 million 
E) 3.97 million

Question 6

You are given the probability that an event will not happen.Find the probability that the event will happen.​ $P \left( E ^ { \prime } \right) = 0.37$ ​

Accepted Answer

A) 0.73 
B) 0.63 
C) 0.83 
D) 0.68 
E) 0.78 
A) 0.73 
B) 0.63 
C) 0.83 
D) 0.68 
E) 0.78

Question 7

There were approximately 28 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.What is the probability that a person selected at random from the population of unemployed workers is in the 45-64 age group.( $a = 28 \%$ and $b = 38 \%$ )

Accepted Answer

A)  $\frac { 1 } { 38 }$ 
B)  $\frac { 19 } { 50 }$ 
C)  $\frac { 50 } { 19 }$ 
D) 38 
E)  $\frac { 1 } { 100 }$ 
A)  $\frac { 1 } { 38 }$ 
B)  $\frac { 19 } { 50 }$ 
C)  $\frac { 50 } { 19 }$ 
D) 38 
E)  $\frac { 1 } { 100 }$

Question 8

​A study of the effectiveness of a flu vaccine was conducted with a sample of 464 people.Some participants in the study were given no vaccine,some were given one injection,and some were given two injections.The results of the study are listed in the table. ​
$$\begin{array} { | l | l | l | l | l | } 
\hline & \begin{array} { l } 
\text { No } \
\text { vaccine }
\end{array} & \begin{array} { l } 
\text { One } \
\text { injection }
\end{array} & \begin{array} { l } 
\text { Two } \
\text { njections }
\end{array} & \text { Total } \
\hline \text { Flu } & 8 & 5 & 12 & 25 \
\hline \text { No flu } & 135 & 41 & 263 & 439 \
\hline \text { Total } & 143 & 46 & 275 & 464 \
\hline
\end{array}$$
A person is selected at random from the sample.Find the probability that the person had two injections.Round your anser to one decimal place.

Accepted Answer

A) ​275.0% 
B) ​63.3% 
C) ​71.3% 
D) ​67.3% 
E) ​59.3% 
A) ​275.0% 
B) ​63.3% 
C) ​71.3% 
D) ​67.3% 
E) ​59.3%

Question 9

You are given the probability that an event will not happen.Find the probability that the event will happen.​ $P \left( E ^ { \prime } \right) = 0.75$ ​

Accepted Answer

A) 0.4 
B) 0.25 
C) 0.35 
D) 0.3 
E) 0.45 
A) 0.4 
B) 0.25 
C) 0.35 
D) 0.3 
E) 0.45

Question 10

You are given the probability that an event will happen.Find the probability that the event will not happen.​ $$P ( E ) = \frac { 1 } { 5 }$$ ​

Accepted Answer

A)  $$\frac { 9 } { 5 }$$ 
B) ​ $$\frac { 3 } { 5 }$$ 
C) ​ $\frac { 1 } { 5 }$ 
D)  $\frac { 2 } { 5 }$ 
E)  $\frac { 4 } { 5 }$ 
A)  $$\frac { 9 } { 5 }$$ 
B) ​ $$\frac { 3 } { 5 }$$ 
C) ​ $\frac { 1 } { 5 }$ 
D)  $\frac { 2 } { 5 }$ 
E)  $\frac { 4 } { 5 }$

Question 11

111 college students were interviewed to determine their political party affiliations and whether they favored a balanced-budget amendment to the Constitution.The results of the study are listed in the table,where D represents Democrat and represents Republican. $$\begin{array} { | l | l | l | l | l | } 
\hline & \text { Favor } & \text { Not favor } & \text { Unsure } & \text { Total } \
\hline \boldsymbol { D } & 24 & 28 & 8 & 60 \
\hline \boldsymbol { R } & 31 & 15 & 5 & 51 \
\hline \text { Total } & 55 & 43 & 13 & 111 \
\hline
\end{array}$$
A person is selected at random from the sample.Find the probability that the described person is selected.A Democrat who favors the amendment.Round your answer to one decimal place.
​

Accepted Answer

A) 22.2% 
B) 21.6% 
C) 21.3% 
D) 24.0% 
E) 24.9% 
A) 22.2% 
B) 21.6% 
C) 21.3% 
D) 24.0% 
E) 24.9%

Question 12

You are given the probability that an event will happen.Find the probability that the event will not happen.​ $P ( E ) = \frac { 11 } { 35 }$ ​

Accepted Answer

A)  $\frac { 11 } { 35 }$ 
B)  $\frac { 35 } { 24 }$ 
C)  $\frac { 8 } { 35 }$ 
D)  $\frac { 24 } { 35 }$ 
E)  $\frac { 35 } { 11 }$ 
A)  $\frac { 11 } { 35 }$ 
B)  $\frac { 35 } { 24 }$ 
C)  $\frac { 8 } { 35 }$ 
D)  $\frac { 24 } { 35 }$ 
E)  $\frac { 35 } { 11 }$

Question 13

The figure shows the results of a recent survey in which 14 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability the adult will give the U.S.public schools a C or a D? ( $a = 14 \%$ , $b = 50 \%$ )   ​

Accepted Answer

A)  $\frac { 16 } { 25 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 50 } { 7 }$ 
D)  $\frac { 25 } { 16 }$ 
E)  $\frac { 7 } { 50 }$ 
A)  $\frac { 16 } { 25 }$ 
B)  $\frac { 1 } { 2 }$ 
C)  $\frac { 50 } { 7 }$ 
D)  $\frac { 25 } { 16 }$ 
E)  $\frac { 7 } { 50 }$

Question 14

Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing 3 green,5 yellow and 4 red marbles such that both marbles are yellow.

Accepted Answer

A) ​ $$\frac { 2 } { 5 }$$ 
B) ​ $$\frac { 5 } { 7 }$$ 
C) ​ $\frac { 25 } { 144 }$ 
D) ​ $\frac { 25 } { 132 }$ 
E) ​ $\frac { 5 } { 33 }$ 
A) ​ $$\frac { 2 } { 5 }$$ 
B) ​ $$\frac { 5 } { 7 }$$ 
C) ​ $\frac { 25 } { 144 }$ 
D) ​ $\frac { 25 } { 132 }$ 
E) ​ $\frac { 5 } { 33 }$

Question 15

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 8.0 million in 2007 and let $a = 8.0 \%$ , $b = 19.9 \%$ and $c = 9.5 \%$ .Find the probability that a person 25 years or older selected at random has earned a Bachelor's degree or higher.​   ​

Accepted Answer

A) 0.294 
B) 1.294 
C) 4.294 
D) 2.294 
E) 3.294 
A) 0.294 
B) 1.294 
C) 4.294 
D) 2.294 
E) 3.294

Question 16

A study of the effectiveness of a flu vaccine was conducted with a sample of 503 people.Some participants in the study were given no vaccine,some were given one injection,and some were given two injections.The results of the study are listed in the table. $$\begin{array} { | l | l | l | l | l | } 
\hline & \text { No vaccine } & \text { One injection } & \text { Two injections } & \text { Total } \
\hline \text { Flu } & 9 & 5 & 19 & 33 \
\hline \text { No flu } & 148 & 60 & 262 & 470 \
\hline \text { Total } & 157 & 65 & 281 & 503 \
\hline
\end{array}$$
A person is selected at random from the sample.Find the specified probability that the person did not get the flu.Round your anser to one decimal place.

Accepted Answer

A) 81.4% 
B) 89.4% 
C) 85.4% 
D) 77.4% 
E) 93.4% 
A) 81.4% 
B) 89.4% 
C) 85.4% 
D) 77.4% 
E) 93.4%

Question 17

​You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 28 } { 40 }$

Accepted Answer

A) ​ $\frac { 7 } { 10 }$ 
B) ​1 
C) ​ $\frac { 3 } { 20 }$ 
D) ​0 
E) ​ $\frac { 3 } { 10 }$ 
A) ​ $\frac { 7 } { 10 }$ 
B) ​1 
C) ​ $\frac { 3 } { 20 }$ 
D) ​0 
E) ​ $\frac { 3 } { 10 }$

Question 18

You are given the probability that an event will happen.Find the probability that the event will not happen.​ $$P ( E ) = \frac { 6 } { 7 }$$ ​

Accepted Answer

A)  $\frac { 6 } { 7 }$ 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  $\frac { 3 } { 7 }$ 
E)  $\frac { 1 } { 7 }$ 
A)  $\frac { 6 } { 7 }$ 
B)  $\frac { 5 } { 7 }$ 
C)  $\frac { 4 } { 7 }$ 
D)  $\frac { 3 } { 7 }$ 
E)  $\frac { 1 } { 7 }$

Question 19

The educational attainment of a country population age 25 years or older in 2007 is shown in the circle graph.Use the fact that the population of people 25 years or older was approximately 293.32 million in 2007.Estimate the number of people 25 years or older who have high school diplomas.Round your anser to two decimal places.​   ​

Accepted Answer

A) 261.38 million 
B) 251.38 million 
C) 291.38 million 
D) 271.38 million 
E) 281.38 million 
A) 261.38 million 
B) 251.38 million 
C) 291.38 million 
D) 271.38 million 
E) 281.38 million

Question 20

The figure shows the results of a survey in which auto racing fans listed their favorite type of racing.What is the probability that an auto racing fan selected at random lists NASCAR racing as his or her favorite type of racing? ( $a = 58 \%$ , $b = 14 \%$ )​   ​

Accepted Answer

A)  $\frac { 18 } { 25 }$ 
B)  $\frac { 5 } { 29 }$ 
C)  $\frac { 29 } { 5 }$ 
D)  $\frac { 50 } { 29 }$ 
E)  $\frac { 29 } { 50 }$ 
A)  $\frac { 18 } { 25 }$ 
B)  $\frac { 5 } { 29 }$ 
C)  $\frac { 29 } { 5 }$ 
D)  $\frac { 50 } { 29 }$ 
E)  $\frac { 29 } { 50 }$

Exam 58: Probability

You are given the probability that an event will happen.Find the probability that the event will not happen. P(E)=0.87P ( E ) = 0.87P(E)=0.87

You are given the probability that an event will happen.Find the probability that the event will not happen.​ P(E)=0.78P ( E ) = 0.78P(E)=0.78 ​

There were approximately 6.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.Estimate the number of unemployed workers in the 16-19 age group.(Round your answer to two decimal places. )​ ​

You are given the probability that an event will not happen.Find the probability that the event will happen.​ P(E′)=0.37P \left( E ^ { \prime } \right) = 0.37P(E′)=0.37 ​

You are given the probability that an event will not happen.Find the probability that the event will happen.​ P(E′)=0.75P \left( E ^ { \prime } \right) = 0.75P(E′)=0.75 ​

You are given the probability that an event will happen.Find the probability that the event will not happen.​ P(E)=15P ( E ) = \frac { 1 } { 5 }P(E)=51​ ​

You are given the probability that an event will happen.Find the probability that the event will not happen.​ P(E)=1135P ( E ) = \frac { 11 } { 35 }P(E)=3511​ ​

The figure shows the results of a recent survey in which 14 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability the adult will give the U.S.public schools a C or a D? ( a=14%a = 14 \%a=14% , b=50%b = 50 \%b=50% ) ​

Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing 3 green,5 yellow and 4 red marbles such that both marbles are yellow.

​You are given the probability that an event will not happen.Find the probability that the event will happen. P(E)=2840P ( E ) = \frac { 28 } { 40 }P(E)=4028​

You are given the probability that an event will happen.Find the probability that the event will not happen.​ P(E)=67P ( E ) = \frac { 6 } { 7 }P(E)=76​ ​

The figure shows the results of a survey in which auto racing fans listed their favorite type of racing.What is the probability that an auto racing fan selected at random lists NASCAR racing as his or her favorite type of racing? ( a=58%a = 58 \%a=58% , b=14%b = 14 \%b=14% )​ ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

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Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

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Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

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Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Lines

Introduction to Conics Parabolas

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Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Graphs of Polar Equations

Filters

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.87$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.78$

There were approximately 6.92 million unemployed workers in the United States.The circle graph shows the age profile of these unemployed workers.Estimate the number of unemployed workers in the 16-19 age group.(Round your answer to two decimal places. )

You are given the probability that an event will not happen.Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = 0.37$

You are given the probability that an event will not happen.Find the probability that the event will happen. $P \left( E ^ { \prime } \right) = 0.75$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 1 } { 5 }$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 11 } { 35 }$

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 28 } { 40 }$

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = \frac { 6 } { 7 }$