Deck 3: Probability

Question 1

A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:
$$\begin{array} { l | c } \text { Color } & \text { Number } \\\hline \text { Red } & 25 \\\text { Brown } & 20 \\\text { Green } & 20 \\\text { Blue } & 15 \\\text { Yellow } & 10 \\\text { Orange } & 10\end{array}$$ 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

Answer 1

0.20

Question 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

Answer 2

0.94

Question 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

Answer 3

0.0600

Question 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

Question 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

Question 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

Question 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. 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

Question 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) $A \cap B$
B) $B ^ { C }$
C) $A ^ { c }$
D) $A \cup B$

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

Question 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

Question 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.
What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile?

A) $215 / 350$
B) $15 / 205$
C) $230 / 350$
D) $15 / 350$

Question 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

Question 13

Which quantity is represented on the screen below?

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

Question 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.


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) $165 / 130$

Question 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. 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

Question 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.

Question 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

Question 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

Question 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) $P ( A ) = \frac { 1 } { 5 } , P ( B ) = \frac { 1 } { 9 } , P ( C ) = \frac { 1 } { 6 }$

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

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

D) $P ( A ) = - \frac { 1 } { 4 } , P ( B ) = \frac { 1 } { 2 } , P ( C ) = \frac { 3 } { 4 }$

Question 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.
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) $20 / 130$
B) $20 / 65$
C) $75 / 130$
D) $20 / 30$

Question 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.

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

A) $65 / 110$
B) $65 / 350$
C) $45 / 350$
D) $65 / 205$

Question 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.
$$\begin{array} { | l | c | } \hline { \text { Type of Book } } & \text { Number } \\\hline \text { Children's } & 51,033 \\\hline \text { Fiction } & 141,114 \\\hline \text { Nonfiction } & 253,074 \\\hline \text { Educational } & 67,252 \\\hline\end{array}$$ 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?

Question 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.

Question 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 $A ^ { C }$ .
b. Identify the sample points in the event $A ^ { C }$ .
c. Find $P \left( A ^ { C } \right)$ .

Question 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.

Question 26

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.

A) 0.60
B) 0.40
C) 0.15
D) 0.85

Question 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.
$$\begin{array} { | l | c | } \hline { \text { Type of Car } } & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array}$$ 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 $A \cup B$ .
b. Identify the sample points in the event $A \cap B$ .
c. Find $P ( A \cup B )$ .
d. Find $P ( A \cap B )$ .

Question 28

Which expression is equal to $\left( \begin{array} { l } N \\ n \end{array} \right)$ ?

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

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

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

D) $\frac { N ! } { N ! ( N - n ) ! }$

Question 29

Suppose that for a certain experiment $P ( A ) = .37 , P ( B ) = .69$ , and $P ( A \cap B ) = .23$ . Find $P ( A \cup$ $B )$ .

Question 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.
$$\begin{array} { l l l l l l l l l l } 39 & 51 & 59 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 90 & 91 & 91 & 92 & 95 & 96 & 97 & 97 & 98\end{array}$$ 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?

Question 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.

Question 32

Which number could be the probability of an event that rarely occurs?

A) - .01
B) .51
C) .99
D) .01

Question 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?

Question 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.

Question 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).

Question 36

Suppose that for a certain experiment

Question 37

A bag of candy was opened and the number of pieces was counted. The results are shown in the table below:
$$\begin{array} { l | c } \text { Color } & \text { Number } \\\hline \text { Red } & 25 \\\text { Brown } & 20 \\\text { Green } & 20 \\\text { Blue } & 15 \\\text { Yellow } & 10 \\\text { Orange } & 10\end{array}$$ 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}

Question 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.

Question 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.

Question 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.

Question 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?

Question 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.

Question 43

$\text { Compute } \left( \begin{array} { l } 5 \\1\end{array} \right)$

Question 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.

Question 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 $A = \{$ Three heads are observed $\}$ .
d. Find the probability of the event $B =$ Exactly two heads are observed $\}$ .
e. Find the probability of the event $C = \{$ At least two heads are observed $\}$

Question 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.

Question 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}

Question 48

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 $P ( B )$ .

Question 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. $$\begin{array} { l l l l l l l l l } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array}$$ 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?

Question 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.

Question 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.

Question 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. $$\begin{array}{l}\begin{array} { | l | l | l | l | l | l | l | } \hline \text { Outcome } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \text { Probability } & .1 & .1 & .1 & .2 & .2 & .3 \\\hline\end{array}\\\end{array}$$
$\text { Find } P ( A \mid B )$

Question 53

Suppose that for a certain experiment $P ( A ) = .8 \text { and } P ( B ) = .9$ Use the Additive Rule to explain why the events A and B can not be mutually exclusive.

Question 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.

Question 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}. $$\text { Is } P ( A \cup B ) \text { equal to the sum of } P ( A ) \text { and } P ( B ) \text { ? Explain. }$$

Question 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 $A ^ { C }$ .
b. Identify the sample points in the event $B ^ { C }$ .
c. Identify the sample points in the event $A ^ { C } \cup B ^ { C }$ .
d. Identify the sample points in the event $A ^ { C } \cap B ^ { C }$ .
e. Find $P \left( A ^ { C } \cup B ^ { C } \right)$ .
f. Find $P \left( A ^ { C } \cap B ^ { C } \right)$ .

Question 57

Question 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?

Question 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.

Question 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$$\text { Region }$
$\begin{array}{rcccr} \hline && \text { NE } & \text { SE } & \text { SW } & \text { NW } \\\hline&<10,000 & 5 \% & 6 \% & 3 \% & 0 \% \\\text { Population of City } 10,000& -100,000 & 15 \% & 6 \% & 12 \% & 5 \% \\&>100,000 & 20 \% & 4 \% & 7 \% & 17 \% \\\hline\end{array}$
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?

Question 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.

Question 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} $$\text { Find } P ( A \mid B ) \text { and } P ( B \mid A ) \text {. }$$

Question 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?

Question 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.

Question 65

In how many ways can a manager choose 3 of his 8 employees to work overtime helping with inventory?

Question 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.

Question 67

Question 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.
$$\begin{array} { c c c c c c c c c } 1 & 2 & 3 & 3 & 4 & 9 & 9 & 11 & 11 \\11 & 14 & 14 & 19 & 22 & 23 & 24 & 25 & 29\end{array}$$
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?

Question 69

Suppose that for a certain experiment

Question 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.
$$\begin{array} { | l | c | } \hline { \text { Type of Car } } & \text { Number } \\\hline \text { Sedan } & 7,204 \\\hline \text { Convertible } & 9,089 \\\hline \text { Wagon } & 20,418 \\\hline \text { SUV } & 13,691 \\\hline \text { Van } & 15,837 \\\hline \text { Hatchback } & 15,350 \\\hline \text { Total } & 81,589 \\\hline\end{array}$$ 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} $$\text { Is } P ( A \cup B ) \text { equal to the sum of } P ( A ) \text { and } P ( B ) \text { ? Explain. }$$

Question 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.

Question 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.).
$$\begin{array} { c c } \text { Simple Events } & \text { Probabilities } \\\text { SS } & 0.58 \\S D & 0.12 \\D S & 0.10 \\D D & 0.20\end{array}$$ Find the probability that neither patient survives.

Question 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.
$$\begin{array} { l l l l l l l } \text { gold } & \text { gold } & \text { silver } & \text { gold } & \text { bronze } & \text { silver } & \text { silver } \\\text { bronze } & \text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { silver } & \text { gold } \\\text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { bronze } & \text { gold } & \text { silver } \\\text { gold } & \text { gold } & \text { bronze } & \text { bronze } & & &\end{array}$$ 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?

Question 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$ $\text { Political Affiliation }$
$\begin{array}{lccc} \hline && \text { Republican } & \text { Democrat } & \text { Independent } \\\hline &\text { White collar } & 17 \% & 19 \% & 15 \% \\\text { Type of job } \\&\text { Blue Collar } & 9 \% & 6 \% & 34 \% \\\hline\end{array}$
What is the probability that the worker is a white collar Republican?

Question 75

Question 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.
$$\begin{array} { l l l l l l l } \text { gold } & \text { gold } & \text { silver } & \text { gold } & \text { bronze } & \text { silver } & \text { silver } \\\text { bronze } & \text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { silver } & \text { gold } \\\text { gold } & \text { silver } & \text { silver } & \text { bronze } & \text { bronze } & \text { gold } & \text { silver } \\\text { gold } & \text { gold } & \text { bronze } & \text { bronze } & & &\end{array}$$ Given that the medal is not bronze, what is the probability that the medal is gold?

Question 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?

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

Question 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.

Question 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.

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

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