Deck 3: Probability

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سؤال
A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:
 Color  Number  Red 25 Brown 20 Green 20 Blue 15 Yellow 10 Orange 10\begin{array} { l | c } \text { Color } & \text { Number } \\\hline \text { Red } & 25 \\\text { Brown } & 20 \\\text { Green } & 20 \\\text { Blue } & 15 \\\text { Yellow } & 10 \\\text { Orange } & 10\end{array} Find the probability that a randomly selected piece is either yellow or orange in color.

A) 0.10
B) 20
C) 10
D) 0.20
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سؤال
A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he misses the first free-throw shot, then he only has a 70% chance of making the second free-throw he shoots. Suppose this player has been awarded two free-throw shots. Find the probability that he makes at least one of the two shots.

A) 0.94
B) 0.80
C) 0.86
D) 0.72
سؤال
In a particular town, 20% of the homes have monitored security systems. If an alarm is triggered, the security system company will contact the local police to alert them of the alarm. Of all the alarm calls that the local police receive, they only have the manpower to answer 30% of the calls. Suppose we randomly sample one home that was broken into over the last month from this town. What is the probability that this home has a monitored security system and that the police answered the alarm call?

A) 0.9400
B) 0.3000
C) 0.0600
D) 0.2000
سؤال
An insurance company looks at many factors when determining how much insurance will cost for a home. Two of the factors are listed below:
A: {The home's roof is less than 10 years old}
B: {The home has a security system}
In the words of the problem, define the event Bc.

A) The home has a security system
B) The home does not have a security system
C) The home is less than 10 years old
D) The home is not less than 10 years old
سؤال
Suppose two dice, one blue and one red, are rolled and the outcomes of each are recorded. We define the following two events:
A: sum of the roll is 7
B. the result of the blue die is a number greater than 4
Are the two events, A and B, independent events?

A) No
B) Yes
سؤال
Which number could be the probability of an event that occurs about as often as it does not occur?

A) 1
B) 0
C) -.51
D) .51
سؤال
A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below. <strong>A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.   Which of the following events listed would be considered mutually exclusive events?</strong> A) The student is a junior and the student drives a domestic automobile B) The student is a senior and the student drives a domestic automobile. C) The student is a freshman and the student drives a foreign automobile D) The student is a junior and the student is a freshman <div style=padding-top: 35px> Which of the following events listed would be considered mutually exclusive events?

A) The student is a junior and the student drives a domestic automobile
B) The student is a senior and the student drives a domestic automobile.
C) The student is a freshman and the student drives a foreign automobile
D) The student is a junior and the student is a freshman
سؤال
A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.
A: {The number is even}
B: {The number is less than 7}
Which expression represents the event that the number is both even and less than 7?
A) ABA \cap B
B) BCB ^ { C }
C) AcA ^ { c }
D) ABA \cup B
سؤال
A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.
A: {The number is even}
B: {The number is less than 7}
Which expression represents the event that the number is even or less than 7 or both?

A) BCB ^C
B) ACA ^ { C }
C) ABA \cap B
D) ABA \cup B
سؤال
A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he misses the first free-throw shot, then he only has a 70% chance of making the second free-throw he
Shoots. Suppose this player has been awarded two free-throw shots. Are the events, A - the player makes the first shot, and B - the player makes the second shot, independent events?

A) No
B) Yes
سؤال
A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.  <strong>A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.   What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile? </strong> A)  215 / 350  B)  15 / 205  C)  230 / 350  D)  15 / 350  <div style=padding-top: 35px>
What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile?

A) 215/350215 / 350
B) 15/20515 / 205
C) 230/350230 / 350
D) 15/35015 / 350
سؤال
An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment?

A) 1
B) 7
C) 2
D) 6
سؤال
Which quantity is represented on the screen below? <strong>Which quantity is represented on the screen below?  </strong> A) The number of ways two coins can be chosen from six coins B) The number of sample points when a coin is flipped six times C) The number of ways two dice can be rolled D) The number of sample points when a die is rolled and a coin is flipped <div style=padding-top: 35px>

A) The number of ways two coins can be chosen from six coins
B) The number of sample points when a coin is flipped six times
C) The number of ways two dice can be rolled
D) The number of sample points when a die is rolled and a coin is flipped
سؤال
A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.

 A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.    What proportion of the employees are male or have been employed for less than 11 years? A)  42 / 65  ?)  45 / 130  C)  120 / 130  D)  165 / 130 <div style=padding-top: 35px>
What proportion of the employees are male or have been employed for less than 11 years?
A) 42/6542 / 65
?) 45/13045 / 130
C) 120/130120 / 130
D) 165/130165 / 130
سؤال
A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below. <strong>A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.   Given that you know the selected student is in the senior class, find the probability they drive a domestic automobile.</strong> A) 15/350 B) 15/205 C) 25/35 D) 10/35 <div style=padding-top: 35px> Given that you know the selected student is in the senior class, find the probability they drive a domestic automobile.

A) 15/350
B) 15/205
C) 25/35
D) 10/35
سؤال
A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below. A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.  <div style=padding-top: 35px>
سؤال
Which number could be the probability of an event that is almost certain to occur?

A) .99
B) .51
C) .01
D) 1.01
سؤال
Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid?

A) 0.9928
B) 0.9325
C) 0.9552
D) 0.0995
سؤال
Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, and C are the only sample points in the experiment?

A) P(A)=15,P(B)=19,P(C)=16P ( A ) = \frac { 1 } { 5 } , P ( B ) = \frac { 1 } { 9 } , P ( C ) = \frac { 1 } { 6 }

B) P(A)=0,P(B)=19,P(C)=89P ( A ) = 0 , P ( B ) = \frac { 1 } { 9 } , P ( C ) = \frac { 8 } { 9 }

C) P(A)=110,P(B)=110,P(C)=110P ( A ) = \frac { 1 } { 10 } , P ( B ) = \frac { 1 } { 10 } , P ( C ) = \frac { 1 } { 10 }

D) P(A)=14,P(B)=12,P(C)=34P ( A ) = - \frac { 1 } { 4 } , P ( B ) = \frac { 1 } { 2 } , P ( C ) = \frac { 3 } { 4 }
سؤال
A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.  <strong>A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.   Suppose an employee has been randomly selected from this company. Given that the employee is male, find the probability that they have worked for the company for more than 10 years? </strong> A)  20 / 130  B)  20 / 65  C)  75 / 130  D)  20 / 30  <div style=padding-top: 35px>
Suppose an employee has been randomly selected from this company. Given that the employee is male, find the probability that they have worked for the company for more than 10 years?

A) 20/13020 / 130
B) 20/6520 / 65
C) 75/13075 / 130
D) 20/3020 / 30
سؤال
A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.  <strong>A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.    Find the probability that a randomly selected student is both a sophomore and drives a foreign automobile.</strong> A)  65 / 110  B)  65 / 350  C)  45 / 350  D)  65 / 205  <div style=padding-top: 35px>

Find the probability that a randomly selected student is both a sophomore and drives a foreign automobile.

A) 65/11065 / 110
B) 65/35065 / 350
C) 45/35045 / 350
D) 65/20565 / 205
سؤال
The table shows the number of each type of book found at an online auction site during a recent search. Suppose that Juanita randomly chose one book to bid on and then noted its type.
 Type of Book  Number  Children’s 51,033 Fiction 141,114 Nonfiction 253,074 Educational 67,252\begin{array} { | l | c | } \hline { \text { Type of Book } } & \text { Number } \\\hline \text { Children's } & 51,033 \\\hline \text { Fiction } & 141,114 \\\hline \text { Nonfiction } & 253,074 \\\hline \text { Educational } & 67,252 \\\hline\end{array} a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the book was nonfiction or educational?
سؤال
Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows.
A: {Both chips are the same color}
B: {At least one of the chips is blue}
Are A and B independent events? Explain.
سؤال
Two chips are drawn at random and without replacement from a bag containing two blue
chips and two red chips. Event A is defined as follows.
A: {Both chips are red} a. Describe the event ACA ^ { C } .
b. Identify the sample points in the event ACA ^ { C } .
c. Find P(AC)P \left( A ^ { C } \right) .
سؤال
A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the sample space for the experiment.
سؤال
A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: <strong>A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:   Find the probability that a randomly chosen piece of candy is not blue or red.</strong> A) 0.60 B) 0.40 C) 0.15 D) 0.85 <div style=padding-top: 35px> Find the probability that a randomly chosen piece of candy is not blue or red.

A) 0.60
B) 0.40
C) 0.15
D) 0.85
سؤال
The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.
 Type of Car  Number  Sedan 7,204 Convertible 9,089 Wagon 20,418 SUV 13,691 Van 15,837 Hatchback 15,350 Total 81,589\begin{array} { | l | c | } \hline { \text { Type of Car } } & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array} Events A and B are defined as follows.
A: {Convertible, SUV, Van}
B: {Fewer than 10,000 of the type of car were sold in June} a. Identify the sample points in the event ABA \cup B .
b. Identify the sample points in the event ABA \cap B .
c. Find P(AB)P ( A \cup B ) .
d. Find P(AB)P ( A \cap B ) .
سؤال
Which expression is equal to (Nn)\left( \begin{array} { l } N \\ n \end{array} \right) ?

A) N!(Nn)!\frac { N ! } { ( N - n ) ! }

B) N!n!\frac { N ! } { n ! }

C) N!n!(Nn)!\frac { N ! } { n ! ( N - n ) ! }

D) N!N!(Nn)!\frac { N ! } { N ! ( N - n ) ! }
سؤال
Suppose that for a certain experiment P(A)=.37,P(B)=.69P ( A ) = .37 , P ( B ) = .69 , and P(AB)=.23P ( A \cap B ) = .23 . Find P(AP ( A \cup B)B ) .
سؤال
The following data represent the scores of 50 students on a statistics exam. Suppose that one of the 50 students is chosen at random and that student's score is noted.
3951596366686869707171717374767676777879797979808082838383858586868888888889898990909191929596979798\begin{array} { l l l l l l l l l l } 39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98\end{array} a. What is the probability that the student's score is 88?
b. What is the probability that the student's score is less than 60?
c. What is the probability that the student's score is between 70 and 79, inclusive?
سؤال
At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student does not receive some form of government-sponsored financial aid.
سؤال
Which number could be the probability of an event that rarely occurs?

A) - .01
B) .51
C) .99
D) .01
سؤال
The manager of an advertising department has asked her creative team to propose six new ideas for an advertising campaign for a major client. She will choose three of the six proposals to present to the client. (We will refer to the six proposals as A, B, C, D, E, and F.)

a. In how many ways can the manager select the three of the six proposals? List the possibilities.

b. It is unlikely that the manager will randomly select three of the six proposals, but if she does what is the probability that she selects proposals A, D, and E?
سؤال
A certain game has a deck of numbered cards of various colors. The probability of drawing a green card from a well-shuffled deck is .25 and the probability of drawing a card numbered 3 is .1. Assuming that "green" and "3" are independent events, find the probability of drawing a green card numbered 3.
سؤال
The accompanying Venn diagram describes the sample space of a particular experiment
and events A and B. Suppose the sample points are equally likely. Find P(A) and P(B). The accompanying Venn diagram describes the sample space of a particular experiment and events A and B. Suppose the sample points are equally likely. Find P(A) and P(B).  <div style=padding-top: 35px>
سؤال
Suppose that for a certain experiment Suppose that for a certain experiment  <div style=padding-top: 35px>
سؤال
A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:
 Color  Number  Red 25 Brown 20 Green 20 Blue 15 Yellow 10 Orange 10\begin{array} { l | c } \text { Color } & \text { Number } \\\hline \text { Red } & 25 \\\text { Brown } & 20 \\\text { Green } & 20 \\\text { Blue } & 15 \\\text { Yellow } & 10 \\\text { Orange } & 10\end{array} List the sample space for this problem.

A) {Red, Brown, Green, Blue, Yellow, Orange}
B) {Red}
C) {25, 20, 20, 15, 10, 10}
D) {0.25, 0.20, 0.20, 0.15, 0.10, 0.10}
سؤال
In a box of 50 markers, 30 markers are either red or black, 20 are missing their caps, and 12 markers are either red or black and are missing their caps. Are the events "red or black" and "missing cap" dependent or independent? Explain.
سؤال
At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student receives some form of government-sponsored financial aid.
سؤال
Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows.
A: {Both chips are red}
B: {At least one of the chips is blue}
Are the events A and B mutually exclusive? Explain.
سؤال
Three companies (A, B, and C) are to be ranked first, second, and third in a list of companies with the highest customer satisfaction.
a. List all the possible sets of rankings for these top three companies.
b. Assuming that all sets of rankings are equally likely, what is the probability that Company A will be ranked first, Company B second, and Company C third?
c. Assuming that all sets of rankings are equally likely, what is the probability that Company B will be ranked first?
سؤال
Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a fish that weighs less than 5 pounds is .45. Is enough information available to find the probability of catching a red snapper or a fish that weighs less than 5 pounds? Explain. If possible, find the probability of catching a red snapper or a fish that weighs less than 5 pounds.
سؤال
 Compute (51)\text { Compute } \left( \begin{array} { l } 5 \\1\end{array} \right)
سؤال
If 80% of a website's visitors are teenagers and 60% of those teenaged visitors are male, find the percentage of the website's visitors that are teenaged males.
سؤال
Three fair coins are tossed and either heads (H) or tails (T) is observed for each coin.
a. List the sample points for this experiment.
b. Assign probabilities to the sample points.
c. Find the probability of the event A={A = \{ Three heads are observed }\} .
d. Find the probability of the event B=B = Exactly two heads are observed }\} .
e. Find the probability of the event C={C = \{ At least two heads are observed }\}
سؤال
In an exit poll, 45% of voters said that the main issue affecting their choices of candidates was the economy, 35% said national security, and the remaining 20% were not sure.
Suppose we select one of the voters who participated in the exit poll at random and ask for the main issue affecting his or her choices of candidates.
a. List the sample points for this experiment.
b. Assign reasonable probabilities to the sample points.
c. Find the probability that the main issue affecting his or her choices was either the economy or national security.
سؤال
A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The sum of the numbers on the dice is 6}
B: {At least one of the numbers 3} A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 6} B: {At least one of the numbers 3}  <div style=padding-top: 35px>
سؤال
The accompanying Venn diagram describes the sample space of a particular experiment and events AA and BB . Suppose P(1)=P(2)=P(3)=P(4)=116P ( 1 ) = P ( 2 ) = P ( 3 ) = P ( 4 ) = \frac { 1 } { 16 } and P(5)=P(6)=P(7)=P(8)=P ( 5 ) = P ( 6 ) = P ( 7 ) = P ( 8 ) = P(9)=P(10)=18.P ( 9 ) = P ( 10 ) = \frac { 1 } { 8 } . Find P(A)P ( A ) and P(B)P ( B ) .


 The accompanying Venn diagram describes the sample space of a particular experiment and events  A  and  B . Suppose  P ( 1 ) = P ( 2 ) = P ( 3 ) = P ( 4 ) = \frac { 1 } { 16 }  and  P ( 5 ) = P ( 6 ) = P ( 7 ) = P ( 8 ) =   P ( 9 ) = P ( 10 ) = \frac { 1 } { 8 } .  Find  P ( A )  and  P ( B ) .     <div style=padding-top: 35px>
سؤال
The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. 12334991111111414192223242529\begin{array} { l l l l l l l l l } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array} Suppose that one of the countries represented is selected at random and the total number of medals won by that country is noted. What is the probability that the country won at least 25 medals given that the country did not win fewer than 10 medals?
سؤال
A company evaluates its potential new employees using three criteria.
A: The applicant has a minimum college GPA of 3.0.
B: The applicant has relevant work experience.
D: The applicant has a sufficient score on an aptitude test. A company evaluates its potential new employees using three criteria. A: The applicant has a minimum college GPA of 3.0. B: The applicant has relevant work experience. D: The applicant has a sufficient score on an aptitude test.  <div style=padding-top: 35px>
سؤال
A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The sum of the numbers showing is odd}
B: {The sum of the numbers showing is 2, 11, or 12}
Are A and B independent events? Explain.
سؤال
The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Let A be the event that the number rolled is less than 4, and let B be the event that the number rolled is odd.  Outcome 123456 Probability .1.1.1.2.2.3\begin{array}{l}\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Outcome } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Probability } & .1 & .1 & .1 & .2 & .2 & .3 \\\hline\end{array}\\\end{array}
 Find P(AB)\text { Find } P ( A \mid B )
سؤال
Suppose that for a certain experiment P(A)=.8 and P(B)=.9P ( A ) = .8 \text { and } P ( B ) = .9 Use the Additive Rule to explain why the events A and B can not be mutually exclusive.
سؤال
A human gene carries a certain disease from a mother to her child with a probability rate of 0.40. That is, there is a 40% chance that the child becomes infected with the disease.
Suppose a female carrier of the gene has four children. Assume that the infections, or lack thereof, are independent of one another. Find the probability that none of the children get the disease from their mother.
سؤال
Three fair coins are tossed and either heads or tails is observed for each coin. Events A and B are defined as follows.
A: {Three heads are observed}.
B: {Exactly two heads are observed}.  Is P(AB) equal to the sum of P(A) and P(B) ? Explain. \text { Is } P ( A \cup B ) \text { equal to the sum of } P ( A ) \text { and } P ( B ) \text { ? Explain. }
سؤال
A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The two numbers rolled are different}
B: {At least one of the numbers is greater than 2} a. Identify the sample points in the event ACA ^ { C } .
b. Identify the sample points in the event BCB ^ { C } .
c. Identify the sample points in the event ACBCA ^ { C } \cup B ^ { C } .
d. Identify the sample points in the event ACBCA ^ { C } \cap B ^ { C } .
e. Find P(ACBC)P \left( A ^ { C } \cup B ^ { C } \right) .
f. Find P(ACBC)P \left( A ^ { C } \cap B ^ { C } \right) .
سؤال
 <div style=padding-top: 35px>
سؤال
The manager of a warehouse club estimates that 7 out of 10 customers will donate a dollar to help a children's hospital during an annual drive to benefit the hospital. Using the manager's estimate, what is the probability that a randomly selected customer will not donate a dollar?
سؤال
Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a grouper is .19. Is enough information available to find the probability of catching a red snapper or a grouper? Explain. If possible, find the probability of catching a red snapper or a grouper.
سؤال
A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich. \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad  Region \text { Region }
 NE  SE  SW  NW <10,0005%6%3%0% Population of City 10,000100,00015%6%12%5%>100,00020%4%7%17%\begin{array}{rcccr} \hline && \text { NE } & \text { SE } & \text { SW } & \text { NW } \\\hline&<10,000 & 5 \% & 6 \% & 3 \% & 0 \% \\\text { Population of City } 10,000& -100,000 & 15 \% & 6 \% & 12 \% & 5 \% \\&>100,000 & 20 \% & 4 \% & 7 \% & 17 \% \\\hline\end{array}
What is the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States?
سؤال
A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The two numbers rolled are different}
B: {At least one of the numbers is greater than 2}
Are the events A and B mutually exclusive? Explain.
سؤال
A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.
A: {The number is even}
B: {The number is less than 7}  Find P(AB) and P(BA)\text { Find } P ( A \mid B ) \text { and } P ( B \mid A ) \text {. }
سؤال
Suppose that 62% of the employees at a company are male and that 35% of the employees just received merit raises. If 20% of the employees are male and received a merit raise, what is the probability that a randomly chosen employee is male given that the employee received a merit raise?
سؤال
At a certain university, 70% of the students own cars. However, only 45% of the residence hall students own cars. Are the events owning a car and living in a residence hall independent? Explain.
سؤال
In how many ways can a manager choose 3 of his 8 employees to work overtime helping with inventory?
سؤال
An experiment consists of randomly choosing a number between 1 and 10. Let A be the event that the number chosen is less than or equal to 7. List the sample points in A.
سؤال
 <div style=padding-top: 35px>
سؤال
The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Suppose that one of the countries represented is chosen at random and the total numbers of medals won by that country is noted.
12334991111111414192223242529\begin{array} { c c c c c c c c c } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array}
a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the country won at least 20 total medals?
سؤال
Suppose that for a certain experiment Suppose that for a certain experiment  <div style=padding-top: 35px>
سؤال
The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.
 Type of Car  Number  Sedan 7,204 Convertible 9,089 Wagon 20,418 SUV 13,691 Van 15,837 Hatchback 15,350 Total 81,589\begin{array} { | l | c | } \hline { \text { Type of Car } } & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array} Events A and B are defined as follows.
A: {Convertible, SUV, Van}
B: {Fewer than 10,000 of the type of car were sold in June}  Is P(AB) equal to the sum of P(A) and P(B) ? Explain. \text { Is } P ( A \cup B ) \text { equal to the sum of } P ( A ) \text { and } P ( B ) \text { ? Explain. }
سؤال
A college has 85 male and 75 female fulltime faculty members. Suppose one fulltime faculty member is selected at random and the faculty member's gender is observed.
a. List the sample points for this experiment.
b. Assign probabilities to the sample points.
سؤال
A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.).
 Simple Events  Probabilities  SS 0.58SD0.12DS0.10DD0.20\begin{array} { c c } \text { Simple Events } & \text { Probabilities } \\\text { SS } & 0.58 \\S D & 0.12 \\D S & 0.10 \\D D & 0.20\end{array} Find the probability that neither patient survives.
سؤال
The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal noted.
 gold  gold  silver  gold  bronze  silver  silver  bronze  gold  silver  silver  bronze  silver  gold  gold  silver  silver  bronze  bronze  gold  silver  gold  gold  bronze  bronze \begin{array} { l l l l l l l } \text { gold } & \text { gold } & \text { silver } & \text { gold } & \text { bronze } & \text { silver } & \text { silver } \\\text { bronze } & \text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { silver } & \text { gold } \\\text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { bronze } & \text { gold } & \text { silver } \\\text { gold } & \text { gold } & \text { bronze } & \text { bronze } & & &\end{array} a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the medal was not bronze?
سؤال
The table shows the political affiliations and types of jobs for workers in a particular state.
Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted.
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad  Political Affiliation \text { Political Affiliation }
 Republican  Democrat  Independent  White collar 17%19%15% Type of job  Blue Collar 9%6%34%\begin{array}{lccc} \hline && \text { Republican } & \text { Democrat } & \text { Independent } \\\hline &\text { White collar } & 17 \% & 19 \% & 15 \% \\\text { Type of job } \\&\text { Blue Collar } & 9 \% & 6 \% & 34 \% \\\hline\end{array}
What is the probability that the worker is a white collar Republican?
سؤال
 <div style=padding-top: 35px>
سؤال
The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal
noted.
 gold  gold  silver  gold  bronze  silver  silver  bronze  gold  silver  silver  bronze  silver  gold  gold  silver  silver  bronze  bronze  gold  silver  gold  gold  bronze  bronze \begin{array} { l l l l l l l } \text { gold } & \text { gold } & \text { silver } & \text { gold } & \text { bronze } & \text { silver } & \text { silver } \\\text { bronze } & \text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { silver } & \text { gold } \\\text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { bronze } & \text { gold } & \text { silver } \\\text { gold } & \text { gold } & \text { bronze } & \text { bronze } & & &\end{array} Given that the medal is not bronze, what is the probability that the medal is gold?
سؤال
Suppose that 80% of the employees of a company received cash or company stock as a bonus at the end of the year. If 60% of the employees received a cash bonus and 30% received stock, what is the probability that a randomly chosen employee received both cash and stock as a bonus?
سؤال
The table shows the number of each car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.
 Type of Car  Number  Sedan 7,204 Convertible 9,089 Wagon 20,418 SUV 13,691 Van 15,837 Hatchback 15,350 Total 81,589\begin{array} { | l | c | } \hline { \text { Type of Car } } & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array} a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the car was a Van or an SUV?
سؤال
On a certain statistics test, 20% of the students earned a score of 90 or above. It was also true that 20% of the male students earned a score of 90 or above. Are the events earning a score of 90 or above and being male independent? Explain.
سؤال
The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.

 Type of Car  Number  Sedan 7,204 Convertible 9,089 Wagon 20,418 SUV 13,691 Van 15,837 Hatchback 15,350 Total 81,589\begin{array}{|l|c|}\hline{\text { Type of Car }} & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array}

Event AA is defined as follows.
A: {Convertible, SUV, Van}
a. Identify the sample points in the event ACA ^ { C } .
b. Find P(Ac)P \left( A ^ { c } \right) .
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Deck 3: Probability
1
A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:
 Color  Number  Red 25 Brown 20 Green 20 Blue 15 Yellow 10 Orange 10\begin{array} { l | c } \text { Color } & \text { Number } \\\hline \text { Red } & 25 \\\text { Brown } & 20 \\\text { Green } & 20 \\\text { Blue } & 15 \\\text { Yellow } & 10 \\\text { Orange } & 10\end{array} Find the probability that a randomly selected piece is either yellow or orange in color.

A) 0.10
B) 20
C) 10
D) 0.20
0.20
2
A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he misses the first free-throw shot, then he only has a 70% chance of making the second free-throw he shoots. Suppose this player has been awarded two free-throw shots. Find the probability that he makes at least one of the two shots.

A) 0.94
B) 0.80
C) 0.86
D) 0.72
0.94
3
In a particular town, 20% of the homes have monitored security systems. If an alarm is triggered, the security system company will contact the local police to alert them of the alarm. Of all the alarm calls that the local police receive, they only have the manpower to answer 30% of the calls. Suppose we randomly sample one home that was broken into over the last month from this town. What is the probability that this home has a monitored security system and that the police answered the alarm call?

A) 0.9400
B) 0.3000
C) 0.0600
D) 0.2000
0.0600
4
An insurance company looks at many factors when determining how much insurance will cost for a home. Two of the factors are listed below:
A: {The home's roof is less than 10 years old}
B: {The home has a security system}
In the words of the problem, define the event Bc.

A) The home has a security system
B) The home does not have a security system
C) The home is less than 10 years old
D) The home is not less than 10 years old
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5
Suppose two dice, one blue and one red, are rolled and the outcomes of each are recorded. We define the following two events:
A: sum of the roll is 7
B. the result of the blue die is a number greater than 4
Are the two events, A and B, independent events?

A) No
B) Yes
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6
Which number could be the probability of an event that occurs about as often as it does not occur?

A) 1
B) 0
C) -.51
D) .51
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7
A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below. <strong>A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.   Which of the following events listed would be considered mutually exclusive events?</strong> A) The student is a junior and the student drives a domestic automobile B) The student is a senior and the student drives a domestic automobile. C) The student is a freshman and the student drives a foreign automobile D) The student is a junior and the student is a freshman Which of the following events listed would be considered mutually exclusive events?

A) The student is a junior and the student drives a domestic automobile
B) The student is a senior and the student drives a domestic automobile.
C) The student is a freshman and the student drives a foreign automobile
D) The student is a junior and the student is a freshman
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8
A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.
A: {The number is even}
B: {The number is less than 7}
Which expression represents the event that the number is both even and less than 7?
A) ABA \cap B
B) BCB ^ { C }
C) AcA ^ { c }
D) ABA \cup B
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9
A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.
A: {The number is even}
B: {The number is less than 7}
Which expression represents the event that the number is even or less than 7 or both?

A) BCB ^C
B) ACA ^ { C }
C) ABA \cap B
D) ABA \cup B
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10
A basketball player has an 80% chance of making the first free-throw he shoots. If he makes the first free-throw shot, then he has a 90% chance of making the second free-throw he shoots. If he misses the first free-throw shot, then he only has a 70% chance of making the second free-throw he
Shoots. Suppose this player has been awarded two free-throw shots. Are the events, A - the player makes the first shot, and B - the player makes the second shot, independent events?

A) No
B) Yes
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11
A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.  <strong>A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.   What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile? </strong> A)  215 / 350  B)  15 / 205  C)  230 / 350  D)  15 / 350
What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile?

A) 215/350215 / 350
B) 15/20515 / 205
C) 230/350230 / 350
D) 15/35015 / 350
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12
An experiment consists of rolling two dice and summing the resulting values. Which of the following is not a sample point for this experiment?

A) 1
B) 7
C) 2
D) 6
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13
Which quantity is represented on the screen below? <strong>Which quantity is represented on the screen below?  </strong> A) The number of ways two coins can be chosen from six coins B) The number of sample points when a coin is flipped six times C) The number of ways two dice can be rolled D) The number of sample points when a die is rolled and a coin is flipped

A) The number of ways two coins can be chosen from six coins
B) The number of sample points when a coin is flipped six times
C) The number of ways two dice can be rolled
D) The number of sample points when a die is rolled and a coin is flipped
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14
A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.

 A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.    What proportion of the employees are male or have been employed for less than 11 years? A)  42 / 65  ?)  45 / 130  C)  120 / 130  D)  165 / 130
What proportion of the employees are male or have been employed for less than 11 years?
A) 42/6542 / 65
?) 45/13045 / 130
C) 120/130120 / 130
D) 165/130165 / 130
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15
A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below. <strong>A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.   Given that you know the selected student is in the senior class, find the probability they drive a domestic automobile.</strong> A) 15/350 B) 15/205 C) 25/35 D) 10/35 Given that you know the selected student is in the senior class, find the probability they drive a domestic automobile.

A) 15/350
B) 15/205
C) 25/35
D) 10/35
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16
A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below. A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.
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17
Which number could be the probability of an event that is almost certain to occur?

A) .99
B) .51
C) .01
D) 1.01
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18
Suppose the probability of an athlete taking a certain illegal steroid is 10%. A test has been developed to detect this type of steroid and will yield either a positive or negative result. Given that the athlete has taken this steroid, the probability of a positive test result is 0.995. Given that the athlete has not taken this steroid, the probability of a negative test result is 0.992. Given that a positive test result has been observed for an athlete, what is the probability that they have taken this steroid?

A) 0.9928
B) 0.9325
C) 0.9552
D) 0.0995
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19
Which of the following assignments of probabilities to the sample points A, B, and C is valid if A, B, and C are the only sample points in the experiment?

A) P(A)=15,P(B)=19,P(C)=16P ( A ) = \frac { 1 } { 5 } , P ( B ) = \frac { 1 } { 9 } , P ( C ) = \frac { 1 } { 6 }

B) P(A)=0,P(B)=19,P(C)=89P ( A ) = 0 , P ( B ) = \frac { 1 } { 9 } , P ( C ) = \frac { 8 } { 9 }

C) P(A)=110,P(B)=110,P(C)=110P ( A ) = \frac { 1 } { 10 } , P ( B ) = \frac { 1 } { 10 } , P ( C ) = \frac { 1 } { 10 }

D) P(A)=14,P(B)=12,P(C)=34P ( A ) = - \frac { 1 } { 4 } , P ( B ) = \frac { 1 } { 2 } , P ( C ) = \frac { 3 } { 4 }
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20
A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.  <strong>A medium-sized company characterized their employees based on the sex of the employee and their length of service to the company. The results are summarized in the table below.   Suppose an employee has been randomly selected from this company. Given that the employee is male, find the probability that they have worked for the company for more than 10 years? </strong> A)  20 / 130  B)  20 / 65  C)  75 / 130  D)  20 / 30
Suppose an employee has been randomly selected from this company. Given that the employee is male, find the probability that they have worked for the company for more than 10 years?

A) 20/13020 / 130
B) 20/6520 / 65
C) 75/13075 / 130
D) 20/3020 / 30
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21
A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.  <strong>A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic) and their year in college (freshman, sophomore, junior, or senior). The results are shown in the table below.    Find the probability that a randomly selected student is both a sophomore and drives a foreign automobile.</strong> A)  65 / 110  B)  65 / 350  C)  45 / 350  D)  65 / 205

Find the probability that a randomly selected student is both a sophomore and drives a foreign automobile.

A) 65/11065 / 110
B) 65/35065 / 350
C) 45/35045 / 350
D) 65/20565 / 205
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22
The table shows the number of each type of book found at an online auction site during a recent search. Suppose that Juanita randomly chose one book to bid on and then noted its type.
 Type of Book  Number  Children’s 51,033 Fiction 141,114 Nonfiction 253,074 Educational 67,252\begin{array} { | l | c | } \hline { \text { Type of Book } } & \text { Number } \\\hline \text { Children's } & 51,033 \\\hline \text { Fiction } & 141,114 \\\hline \text { Nonfiction } & 253,074 \\\hline \text { Educational } & 67,252 \\\hline\end{array} a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the book was nonfiction or educational?
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23
Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows.
A: {Both chips are the same color}
B: {At least one of the chips is blue}
Are A and B independent events? Explain.
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24
Two chips are drawn at random and without replacement from a bag containing two blue
chips and two red chips. Event A is defined as follows.
A: {Both chips are red} a. Describe the event ACA ^ { C } .
b. Identify the sample points in the event ACA ^ { C } .
c. Find P(AC)P \left( A ^ { C } \right) .
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25
A package of self-sticking notepads contains 6 yellow, 6 blue, 6 green, and 6 pink notepads. An experiment consists of randomly selecting one of the notepads and recording its color. Find the sample space for the experiment.
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26
A bag of candy was opened and the number of pieces was counted. The results are shown in the table below: <strong>A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:   Find the probability that a randomly chosen piece of candy is not blue or red.</strong> A) 0.60 B) 0.40 C) 0.15 D) 0.85 Find the probability that a randomly chosen piece of candy is not blue or red.

A) 0.60
B) 0.40
C) 0.15
D) 0.85
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27
The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.
 Type of Car  Number  Sedan 7,204 Convertible 9,089 Wagon 20,418 SUV 13,691 Van 15,837 Hatchback 15,350 Total 81,589\begin{array} { | l | c | } \hline { \text { Type of Car } } & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array} Events A and B are defined as follows.
A: {Convertible, SUV, Van}
B: {Fewer than 10,000 of the type of car were sold in June} a. Identify the sample points in the event ABA \cup B .
b. Identify the sample points in the event ABA \cap B .
c. Find P(AB)P ( A \cup B ) .
d. Find P(AB)P ( A \cap B ) .
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28
Which expression is equal to (Nn)\left( \begin{array} { l } N \\ n \end{array} \right) ?

A) N!(Nn)!\frac { N ! } { ( N - n ) ! }

B) N!n!\frac { N ! } { n ! }

C) N!n!(Nn)!\frac { N ! } { n ! ( N - n ) ! }

D) N!N!(Nn)!\frac { N ! } { N ! ( N - n ) ! }
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29
Suppose that for a certain experiment P(A)=.37,P(B)=.69P ( A ) = .37 , P ( B ) = .69 , and P(AB)=.23P ( A \cap B ) = .23 . Find P(AP ( A \cup B)B ) .
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30
The following data represent the scores of 50 students on a statistics exam. Suppose that one of the 50 students is chosen at random and that student's score is noted.
3951596366686869707171717374767676777879797979808082838383858586868888888889898990909191929596979798\begin{array} { l l l l l l l l l l } 39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98\end{array} a. What is the probability that the student's score is 88?
b. What is the probability that the student's score is less than 60?
c. What is the probability that the student's score is between 70 and 79, inclusive?
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31
At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student does not receive some form of government-sponsored financial aid.
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32
Which number could be the probability of an event that rarely occurs?

A) - .01
B) .51
C) .99
D) .01
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33
The manager of an advertising department has asked her creative team to propose six new ideas for an advertising campaign for a major client. She will choose three of the six proposals to present to the client. (We will refer to the six proposals as A, B, C, D, E, and F.)

a. In how many ways can the manager select the three of the six proposals? List the possibilities.

b. It is unlikely that the manager will randomly select three of the six proposals, but if she does what is the probability that she selects proposals A, D, and E?
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34
A certain game has a deck of numbered cards of various colors. The probability of drawing a green card from a well-shuffled deck is .25 and the probability of drawing a card numbered 3 is .1. Assuming that "green" and "3" are independent events, find the probability of drawing a green card numbered 3.
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35
The accompanying Venn diagram describes the sample space of a particular experiment
and events A and B. Suppose the sample points are equally likely. Find P(A) and P(B). The accompanying Venn diagram describes the sample space of a particular experiment and events A and B. Suppose the sample points are equally likely. Find P(A) and P(B).
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36
Suppose that for a certain experiment Suppose that for a certain experiment
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37
A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:
 Color  Number  Red 25 Brown 20 Green 20 Blue 15 Yellow 10 Orange 10\begin{array} { l | c } \text { Color } & \text { Number } \\\hline \text { Red } & 25 \\\text { Brown } & 20 \\\text { Green } & 20 \\\text { Blue } & 15 \\\text { Yellow } & 10 \\\text { Orange } & 10\end{array} List the sample space for this problem.

A) {Red, Brown, Green, Blue, Yellow, Orange}
B) {Red}
C) {25, 20, 20, 15, 10, 10}
D) {0.25, 0.20, 0.20, 0.15, 0.10, 0.10}
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38
In a box of 50 markers, 30 markers are either red or black, 20 are missing their caps, and 12 markers are either red or black and are missing their caps. Are the events "red or black" and "missing cap" dependent or independent? Explain.
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39
At a small private college with 800 students, 240 students receive some form of government-sponsored financial aid. Find the probability that a randomly selected student receives some form of government-sponsored financial aid.
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40
Two chips are drawn at random and without replacement from a bag containing two blue chips and two red chips. Events A and B are defined as follows.
A: {Both chips are red}
B: {At least one of the chips is blue}
Are the events A and B mutually exclusive? Explain.
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41
Three companies (A, B, and C) are to be ranked first, second, and third in a list of companies with the highest customer satisfaction.
a. List all the possible sets of rankings for these top three companies.
b. Assuming that all sets of rankings are equally likely, what is the probability that Company A will be ranked first, Company B second, and Company C third?
c. Assuming that all sets of rankings are equally likely, what is the probability that Company B will be ranked first?
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42
Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a fish that weighs less than 5 pounds is .45. Is enough information available to find the probability of catching a red snapper or a fish that weighs less than 5 pounds? Explain. If possible, find the probability of catching a red snapper or a fish that weighs less than 5 pounds.
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43
 Compute (51)\text { Compute } \left( \begin{array} { l } 5 \\1\end{array} \right)
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44
If 80% of a website's visitors are teenagers and 60% of those teenaged visitors are male, find the percentage of the website's visitors that are teenaged males.
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45
Three fair coins are tossed and either heads (H) or tails (T) is observed for each coin.
a. List the sample points for this experiment.
b. Assign probabilities to the sample points.
c. Find the probability of the event A={A = \{ Three heads are observed }\} .
d. Find the probability of the event B=B = Exactly two heads are observed }\} .
e. Find the probability of the event C={C = \{ At least two heads are observed }\}
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46
In an exit poll, 45% of voters said that the main issue affecting their choices of candidates was the economy, 35% said national security, and the remaining 20% were not sure.
Suppose we select one of the voters who participated in the exit poll at random and ask for the main issue affecting his or her choices of candidates.
a. List the sample points for this experiment.
b. Assign reasonable probabilities to the sample points.
c. Find the probability that the main issue affecting his or her choices was either the economy or national security.
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47
A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The sum of the numbers on the dice is 6}
B: {At least one of the numbers 3} A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 6} B: {At least one of the numbers 3}
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48
The accompanying Venn diagram describes the sample space of a particular experiment and events AA and BB . Suppose P(1)=P(2)=P(3)=P(4)=116P ( 1 ) = P ( 2 ) = P ( 3 ) = P ( 4 ) = \frac { 1 } { 16 } and P(5)=P(6)=P(7)=P(8)=P ( 5 ) = P ( 6 ) = P ( 7 ) = P ( 8 ) = P(9)=P(10)=18.P ( 9 ) = P ( 10 ) = \frac { 1 } { 8 } . Find P(A)P ( A ) and P(B)P ( B ) .


 The accompanying Venn diagram describes the sample space of a particular experiment and events  A  and  B . Suppose  P ( 1 ) = P ( 2 ) = P ( 3 ) = P ( 4 ) = \frac { 1 } { 16 }  and  P ( 5 ) = P ( 6 ) = P ( 7 ) = P ( 8 ) =   P ( 9 ) = P ( 10 ) = \frac { 1 } { 8 } .  Find  P ( A )  and  P ( B ) .
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49
The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. 12334991111111414192223242529\begin{array} { l l l l l l l l l } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array} Suppose that one of the countries represented is selected at random and the total number of medals won by that country is noted. What is the probability that the country won at least 25 medals given that the country did not win fewer than 10 medals?
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50
A company evaluates its potential new employees using three criteria.
A: The applicant has a minimum college GPA of 3.0.
B: The applicant has relevant work experience.
D: The applicant has a sufficient score on an aptitude test. A company evaluates its potential new employees using three criteria. A: The applicant has a minimum college GPA of 3.0. B: The applicant has relevant work experience. D: The applicant has a sufficient score on an aptitude test.
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51
A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The sum of the numbers showing is odd}
B: {The sum of the numbers showing is 2, 11, or 12}
Are A and B independent events? Explain.
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52
The table displays the probabilities for each of the six outcomes when rolling a particular unfair die. Suppose that the die is rolled once. Let A be the event that the number rolled is less than 4, and let B be the event that the number rolled is odd.  Outcome 123456 Probability .1.1.1.2.2.3\begin{array}{l}\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Outcome } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Probability } & .1 & .1 & .1 & .2 & .2 & .3 \\\hline\end{array}\\\end{array}
 Find P(AB)\text { Find } P ( A \mid B )
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53
Suppose that for a certain experiment P(A)=.8 and P(B)=.9P ( A ) = .8 \text { and } P ( B ) = .9 Use the Additive Rule to explain why the events A and B can not be mutually exclusive.
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54
A human gene carries a certain disease from a mother to her child with a probability rate of 0.40. That is, there is a 40% chance that the child becomes infected with the disease.
Suppose a female carrier of the gene has four children. Assume that the infections, or lack thereof, are independent of one another. Find the probability that none of the children get the disease from their mother.
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55
Three fair coins are tossed and either heads or tails is observed for each coin. Events A and B are defined as follows.
A: {Three heads are observed}.
B: {Exactly two heads are observed}.  Is P(AB) equal to the sum of P(A) and P(B) ? Explain. \text { Is } P ( A \cup B ) \text { equal to the sum of } P ( A ) \text { and } P ( B ) \text { ? Explain. }
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56
A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The two numbers rolled are different}
B: {At least one of the numbers is greater than 2} a. Identify the sample points in the event ACA ^ { C } .
b. Identify the sample points in the event BCB ^ { C } .
c. Identify the sample points in the event ACBCA ^ { C } \cup B ^ { C } .
d. Identify the sample points in the event ACBCA ^ { C } \cap B ^ { C } .
e. Find P(ACBC)P \left( A ^ { C } \cup B ^ { C } \right) .
f. Find P(ACBC)P \left( A ^ { C } \cap B ^ { C } \right) .
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57
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58
The manager of a warehouse club estimates that 7 out of 10 customers will donate a dollar to help a children's hospital during an annual drive to benefit the hospital. Using the manager's estimate, what is the probability that a randomly selected customer will not donate a dollar?
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59
Based on past experience, Josh believes that the probability of catching a red snapper is .21 and the probability of catching a grouper is .19. Is enough information available to find the probability of catching a red snapper or a grouper? Explain. If possible, find the probability of catching a red snapper or a grouper.
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60
A fast-food restaurant chain with 700 outlets in the United States has recorded the geographic location of its restaurants in the accompanying table of percentages. One restaurant is to be chosen at random from the 700 to test market a new chicken sandwich. \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad  Region \text { Region }
 NE  SE  SW  NW <10,0005%6%3%0% Population of City 10,000100,00015%6%12%5%>100,00020%4%7%17%\begin{array}{rcccr} \hline && \text { NE } & \text { SE } & \text { SW } & \text { NW } \\\hline&<10,000 & 5 \% & 6 \% & 3 \% & 0 \% \\\text { Population of City } 10,000& -100,000 & 15 \% & 6 \% & 12 \% & 5 \% \\&>100,000 & 20 \% & 4 \% & 7 \% & 17 \% \\\hline\end{array}
What is the probability that the restaurant is located in a city with a population over 100,000, given that it is located in the southwestern United States?
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61
A pair of fair dice is tossed. Events A and B are defined as follows.
A: {The two numbers rolled are different}
B: {At least one of the numbers is greater than 2}
Are the events A and B mutually exclusive? Explain.
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62
A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows.
A: {The number is even}
B: {The number is less than 7}  Find P(AB) and P(BA)\text { Find } P ( A \mid B ) \text { and } P ( B \mid A ) \text {. }
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63
Suppose that 62% of the employees at a company are male and that 35% of the employees just received merit raises. If 20% of the employees are male and received a merit raise, what is the probability that a randomly chosen employee is male given that the employee received a merit raise?
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64
At a certain university, 70% of the students own cars. However, only 45% of the residence hall students own cars. Are the events owning a car and living in a residence hall independent? Explain.
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65
In how many ways can a manager choose 3 of his 8 employees to work overtime helping with inventory?
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66
An experiment consists of randomly choosing a number between 1 and 10. Let A be the event that the number chosen is less than or equal to 7. List the sample points in A.
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67
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68
The data show the total number of medals (gold, silver, and bronze) won by each country winning at least one gold medal in the Winter Olympics. Suppose that one of the countries represented is chosen at random and the total numbers of medals won by that country is noted.
12334991111111414192223242529\begin{array} { c c c c c c c c c } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array}
a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the country won at least 20 total medals?
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69
Suppose that for a certain experiment Suppose that for a certain experiment
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70
The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.
 Type of Car  Number  Sedan 7,204 Convertible 9,089 Wagon 20,418 SUV 13,691 Van 15,837 Hatchback 15,350 Total 81,589\begin{array} { | l | c | } \hline { \text { Type of Car } } & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array} Events A and B are defined as follows.
A: {Convertible, SUV, Van}
B: {Fewer than 10,000 of the type of car were sold in June}  Is P(AB) equal to the sum of P(A) and P(B) ? Explain. \text { Is } P ( A \cup B ) \text { equal to the sum of } P ( A ) \text { and } P ( B ) \text { ? Explain. }
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71
A college has 85 male and 75 female fulltime faculty members. Suppose one fulltime faculty member is selected at random and the faculty member's gender is observed.
a. List the sample points for this experiment.
b. Assign probabilities to the sample points.
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72
A hospital reports that two patients have been admitted who have contracted Crohn's disease. Suppose our experiment consists of observing whether each patient survives or dies as a result of the disease. The simple events and probabilities of their occurrences are shown in the table (where S in the first position means that patient 1 survives, D in the first position means that patient 1 dies, etc.).
 Simple Events  Probabilities  SS 0.58SD0.12DS0.10DD0.20\begin{array} { c c } \text { Simple Events } & \text { Probabilities } \\\text { SS } & 0.58 \\S D & 0.12 \\D S & 0.10 \\D D & 0.20\end{array} Find the probability that neither patient survives.
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73
The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal noted.
 gold  gold  silver  gold  bronze  silver  silver  bronze  gold  silver  silver  bronze  silver  gold  gold  silver  silver  bronze  bronze  gold  silver  gold  gold  bronze  bronze \begin{array} { l l l l l l l } \text { gold } & \text { gold } & \text { silver } & \text { gold } & \text { bronze } & \text { silver } & \text { silver } \\\text { bronze } & \text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { silver } & \text { gold } \\\text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { bronze } & \text { gold } & \text { silver } \\\text { gold } & \text { gold } & \text { bronze } & \text { bronze } & & &\end{array} a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the medal was not bronze?
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74
The table shows the political affiliations and types of jobs for workers in a particular state.
Suppose a worker is selected at random within the state and the worker's political affiliation and type of job are noted.
\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad  Political Affiliation \text { Political Affiliation }
 Republican  Democrat  Independent  White collar 17%19%15% Type of job  Blue Collar 9%6%34%\begin{array}{lccc} \hline && \text { Republican } & \text { Democrat } & \text { Independent } \\\hline &\text { White collar } & 17 \% & 19 \% & 15 \% \\\text { Type of job } \\&\text { Blue Collar } & 9 \% & 6 \% & 34 \% \\\hline\end{array}
What is the probability that the worker is a white collar Republican?
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75
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76
The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal
noted.
 gold  gold  silver  gold  bronze  silver  silver  bronze  gold  silver  silver  bronze  silver  gold  gold  silver  silver  bronze  bronze  gold  silver  gold  gold  bronze  bronze \begin{array} { l l l l l l l } \text { gold } & \text { gold } & \text { silver } & \text { gold } & \text { bronze } & \text { silver } & \text { silver } \\\text { bronze } & \text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { silver } & \text { gold } \\\text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { bronze } & \text { gold } & \text { silver } \\\text { gold } & \text { gold } & \text { bronze } & \text { bronze } & & &\end{array} Given that the medal is not bronze, what is the probability that the medal is gold?
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77
Suppose that 80% of the employees of a company received cash or company stock as a bonus at the end of the year. If 60% of the employees received a cash bonus and 30% received stock, what is the probability that a randomly chosen employee received both cash and stock as a bonus?
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78
The table shows the number of each car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.
 Type of Car  Number  Sedan 7,204 Convertible 9,089 Wagon 20,418 SUV 13,691 Van 15,837 Hatchback 15,350 Total 81,589\begin{array} { | l | c | } \hline { \text { Type of Car } } & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array} a. List the sample points for this experiment.
b. Find the probability of each sample point.
c. What is the probability that the car was a Van or an SUV?
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79
On a certain statistics test, 20% of the students earned a score of 90 or above. It was also true that 20% of the male students earned a score of 90 or above. Are the events earning a score of 90 or above and being male independent? Explain.
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80
The table shows the number of each Ford car sold in the United States in June. Suppose the sales record for one of these cars is randomly selected and the type of car is identified.

 Type of Car  Number  Sedan 7,204 Convertible 9,089 Wagon 20,418 SUV 13,691 Van 15,837 Hatchback 15,350 Total 81,589\begin{array}{|l|c|}\hline{\text { Type of Car }} & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array}

Event AA is defined as follows.
A: {Convertible, SUV, Van}
a. Identify the sample points in the event ACA ^ { C } .
b. Find P(Ac)P \left( A ^ { c } \right) .
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