Deck 58: Probability

Question 1

You are given the probability that an event will happen.Find the probability that the event will not happen.​ $P ( E ) =$ $\frac { 17 } { 20 }$ ​

A) $\frac { 20 } { 17 }$
B) $$\frac { 3 } { 20 }$$
C) $\frac { 17 } { 20 }$
D) $\frac { 1 } { 100 }$
E) $\frac { 20 } { 3 }$

Answer 1

$$\frac { 3 } { 20 }$$

Question 2

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.​ ​

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

Answer 2

0.294

Question 3

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 $b = 38 \%$ )

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

Answer 3

$\frac { 19 } { 50 }$

Question 4

You are given the probability that an event will happen.Find the probability that the event will not happen.​ $$P ( E ) = 0.18$$ ​

A)0.88
B)0.89
C)0.82
D)0.87
E)0.18

Question 5

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

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

Question 6

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

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

Question 7

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

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

Question 8

Determine the sample space for the experiment. ​
A six-sided die is tossed twice and the sum of the results is recorded.
​

A)​{2,3,... ,12}
B)​{3,4,... ,6}
C)​{1,2,... ,6}
D)​{3,4,... ,18}

Question 9

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

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

Question 10

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 6.3 million in 2007 and let $$a = 6.3 \%$$ , $b = 20.5 \%$ , $$c = 11.6 \%$$ and $d = 13.3 \%$ .Find the probability that a person 25 years or older selected at random has earned a Bachelor's degree or higher.​ ​

A)3.321
B)2.321
C)4.321
D)0.321
E)1.321

Question 11

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.​ ​

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

Question 12

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 243.32 million in 2007.Estimate the number of people 25 years or older who have advanced degrees.Round your anser to two decimal places.​ ​

A)24.09 million
B)64.09 million
C)44.09 million
D)54.09 million
E)34.09 million

Question 13

The figure shows the results of a recent survey in which 1040 adults were asked to grade U.S.public schools.Estimate the number of adults who gave U.S.public schools a B.​ ​

A)265
B)260
C)255
D)250
E)270

Question 14

There were approximately 42 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 45 or older? ( $a = 42 \%$ and $b = 39 \%$ )​ ​

A) $\frac { 1 } { 100 }$
B) $\frac { 21 } { 50 }$
C) $\frac { 1 } { 42 }$
D) $\frac { 50 } { 21 }$
E)42

Question 15

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

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

Question 16

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

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

Question 17

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 8.1 million in 2007 and let $a = 8.1 \%$ , $b = 17.8 \%$ , $c = 9.8 \%$ and $d = 16 \%$ .Find the probability that a person 25 years or older selected at random has earned an Associate's degree or higher.

A)0.357
B)0.457
C)0.757
D)0.657
E)0.557

Question 18

The figure shows the results of a recent survey in which 1011 adults were asked to grade U.S.public schools.An adult is selected at random.What is the probability that the adult will give the U.S.public schools an A? ( $a = 3 \%$ , $b = 11 \%$ , $c = 19 \%$ )​ ​

A) $\frac { 100 } { 3 }$
B) $\frac { 3 } { 100 }$
C) $\frac { 1 } { 3 }$
D) $\frac { 3 } { 50 }$
E)100

Question 19

There were approximately 8.92 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) $\frac { 1 } { 100 }$
B) $\frac { 1 } { 50 }$
C) $\frac { 13 } { 50 }$
D) $\frac { 5 } { 3 }$
E)60

Question 20

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. )​ ​

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

Question 21

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.

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

Question 22

118 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 R represents Republican. $$\begin{array} { | l | l | l | l | l | } \hline & \text { Favor } & \text { Not favor } & \text { Unsure } & \text { Total } \\\hline \boldsymbol { D } & 22 & 27 & 6 & 55 \\\hline \boldsymbol { R } & 50 & 6 & 7 & 63 \\\hline \text { Total } & 72 & 33 & 13 & 118 \\\hline\end{array}$$
A person is selected at random from the sample.Find the probability that the described person is selected.A person who doesn't favor the amendment.Round your anser to one decimal place.

A)28.8%
B)25.4%
C)27.9%
D)26.2%
E)28.0%

Question 23

​Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing two green,five yellow,and three red marbles such that the marbles are different colors.

A)​ $\frac { 31 } { 90 }$
B)​ $\frac { 31 } { 15 }$
C)​ $\frac { 31 } { 45 }$
D)​ $\frac { 1 } { 5 }$
E)​ $\frac { 62 } { 9 }$

Question 24

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.

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

Question 25

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.
​

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

Question 26

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 does not list NHRA drag racing as his or her favorite type of racing? ( $a = 55 \%$ , $b = 15 \%$ , $c = 13 \%$ , $d = 6 \%$ )​ ​

A) $\frac { 11 } { 20 }$
B) $\frac { 3 } { 20 }$
C) $\frac { 17 } { 20 }$
D) $\frac { 20 } { 3 }$
E) $\frac { 20 } { 17 }$

Question 27

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.

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

Question 28

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 Formula One $d = 8 \%$ or motorcycle racing $c = 10 \%$ as his or her favorite type of racing? ( $a = 53 \%$ , $b = 18 \%$ )​ ​

A) $\frac { 50 } { 9 }$
B) $\frac { 1 } { 50 }$
C)1
D) $\frac { 9 } { 50 }$
E) $\frac { 2 } { 25 }$

Question 29

117 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 R represents Republican. $$\begin{array} { | l | l | l | l | l | } \hline & \text { Favor } & \text { Not favor } & \text { Unsure } & \text { Total } \\\hline \boldsymbol { D } & 23 & 30 & 7 & 60 \\\hline \boldsymbol { R } & 39 & 13 & 5 & 57 \\\hline \text { Total } & 62 & 43 & 12 & 117 \\\hline\end{array}$$
A person is selected at random from the sample.Find the probability that the described person is selected.A Republican.Round your answer to one decimal place.
​

A)43.3%
B)44.2%
C)48.7%
D)46.8%
E)45.9%

Question 30

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

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

Question 31

Find the probability for the experiment of selecting one card from a standard deck of 52 playing cards such that the card is a 10 or higher (aces are low).

A) $\frac { 3 } { 13 }$
B)​ $\frac { 5 } { 13 }$
C) $\frac { 1 } { 2 }$
D)1
E) $\frac { 4 } { 13 }$

Question 32

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.

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

Question 33

​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.

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

Question 34

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? ( $a = 14 \%$ , $b = 50 \%$ ) ​

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

Question 35

You are given the probability that an event will happen.Find the probability that the event will not happen. $P ( E ) = 0.8$

A)1
B)0.2
C)0.1
D)0.8
E)0

Question 36

Find the probability for the experiment of tossing a six-sided die twice such that the sum is either 7 or 11. ​

A) $\frac { 2 } { 9 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 6 }$
D) $\frac { 5 } { 16 }$
E) $\frac { 7 } { 36 }$

Question 37

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? ( $a = 58 \%$ , $b = 14 \%$ )​ ​

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

Question 38

A college sent a survey to a sample of juniors.Of the 512 students surveyed,279 live on campus,of whom 110 have a GPA of 2.5 or greater.The other 233 juniors live off-campus,of whom 85 have a GPA of 2.5 or greater.What is the probability that a survey participant chosen at random lives on campus and has a GPA of 2.5 or greater?

A) $\frac { 279 } { 512 }$
B) $\frac { 22 } { 39 }$
C) $\frac { 110 } { 279 }$
D) $\frac { 195 } { 512 }$
E) $\frac { 55 } { 256 }$

Question 39

A college sent a survey to a sample of juniors.Of the 620 students surveyed,307 live on campus,of whom 139 have a GPA of 2.5 or greater.The other 313 juniors live off-campus,of whom 153 have a GPA of 2.5 or greater.What is the probability that a survey participant chosen at random has a GPA less than 2.5?

A) $\frac { 307 } { 620 }$
B) $\frac { 139 } { 620 }$
C) $\frac { 82 } { 155 }$
D) $\frac { 139 } { 292 }$
E) $\frac { 139 } { 307 }$

Question 40

In a high school graduating class of 128 students,52 are on the honor roll.Of these,45 are going on to college;of the other 76 students,53 are going on to college.A student is selected at random from the class.What is the probability that the person chosen is going to college. ​

A) $\frac { 49 } { 64 }$
B) $\frac { 64 } { 49 }$
C) $\frac { 53 } { 128 }$
D) $\frac { 128 } { 53 }$
E) $\frac { 45 } { 128 }$

Question 41

Determine the sample space for the experiment. ​
Two prize winners are selected from six people: A,B,C,D,E,and F.
​

A)S = {AB,AC,AD,AE,BC,BD,BE,CD,CE,DE}
B)S = {AB,AC,AD,AE,AF}
C)S = {AB,AC,AD,AE,AF,BC,BD,BE,BF,CD,CE,CF,DE,DF,EF}
D)S = {AB,AC,AD,BC,BD,CD}
E)S = {AB,CD,EF}

Question 42

You are given the probability that an event will not happen.Find the probability that the event will happen. $P ( E ) = \frac { 4 } { 15 }$

A) $\frac { 4 } { 15 }$
B)0
C)1
D) $\frac { 11 } { 15 }$
E) $\frac { 11 } { 30 }$

Question 43

Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing 2 green,6 yellow and 3 red marbles such that both marbles are yellow.

A)​ $\frac { 1 } { 3 }$
B)​ $\frac { 6 } { 5 }$
C)​ $\frac { 36 } { 121 }$
D)​ $\frac { 18 } { 55 }$
E)​ $\frac { 3 } { 11 }$

Question 44

Determine the sample space for the experiment.
Three prize winners are selected from six people: A,B,C,D,E,and F.

Question 45

In a sample of 20 hand-held calculators,15 are known to be nonfunctional.If 7 of these calculators are selected at random,what is the probability that exactly 5 in the selection are nonfunctional? Round to the nearest thousandth.

A)0
B)0.714
C)0.387
D)0.467
E)0.750

Question 46

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

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

Question 47

Find the probability for the experiment of drawing two marbles (without replacement)from a bag containing three green,five yellow,and two red marbles such that the marbles are different colors.

A) $\frac { 31 } { 90 }$
B) $\frac { 31 } { 15 }$
C) $\frac { 31 } { 45 }$
D) $\frac { 1 } { 5 }$
E)0