Question 1

Four hundred accidents that occurred on a Saturday night were analyzed. The number of vehicles involved and whether alcohol played a role in the accident were recorded. The results are shown
Below:

Suppose that one of the 400 accidents is chosen at random. What is the probability that the accident involved more than a single vehicle?

Accepted Answer

The answer of Four hundred accidents that occurred on a...

Question 2

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 3}
B: {At least one of the dice shows a 2}
True or False: $$A \cup B = B$$

Accepted Answer

Event A is a subset of Event B because the only way to get a sum of 3 is by rolling a 1 and a 2, which satisfies the condition of Event B (at least one die shows a 2). Therefore, the union of A and B is just B, as A does not add any new outcomes to B.

Question 3

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}
True or False: $$A \cap B = B .$$

Accepted Answer

The intersection $A \cap B$ represents the event where both chips are red and at least one chip is blue, which is impossible. Therefore, $A \cap B$ is an empty set, not equal to $B$.

Question 4

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?

Accepted Answer

The correct expression for the event that the number is even or less than 7 or both is $A \cup B$, which represents the union of events A and B. This includes all numbers that are either even, less than 7, or both.

Question 5

A consumer advocacy group rates the quality of a cellular service provider using three
criteria.
A: Service is available at least 99% of the time.
B: Reception is clear at least 95% of the time.
C: Fewer than 5% of its customers have complaints about the quality of service. a. Describe the event represented by $A \cap B \cap C$.
b. Describe the event represented by $A \cup B \cup C$.

Accepted Answer

The answer of A consumer advocacy group rates the quality...

Question 6

Unions and intersections of events are examples of compound events.

Accepted Answer

Unions and intersections of events combine two or more events, making them compound events.

Question 7

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.

What is the probability that the restaurant is located in a city with a population over 100,000 and in the southern portion of the United States?

Accepted Answer

The answer of A fast-food restaurant chain with 700 outlets...

Question 8

Fill in the blank. The __________ of two events A and B is the event that both A and B occur.

Accepted Answer

The intersection of two events A and B refers to the set of outcomes that are common to both A and B, meaning it represents the event where both A and B occur.

Question 9

Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The managerʹs educational background was also noted. The data appear below:

If we randomly selected one manager from this company, find the probability that he or she has an advanced (Master's or Ph.D.) degree and is a good manager.

Accepted Answer

The answer of Each manager of a corporation was rated...

Question 10

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?

Accepted Answer

$A \cap B$ represents the intersection of events A and B, which means it includes all outcomes that are both even and less than 7.

Question 11

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.
C: The applicant has a sufficient score on an aptitude test.
a. Write the event that an applicant meets all three criteria as a union or intersection of
A, B, and C.
b. Write the event that an applicant meets at least one of the three criteria as a union or
intersection of A, B, and C.

Accepted Answer

The answer of A company evaluates its potential new employees...

Question 12

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. Find $P ( A \cap B )$.

Accepted Answer

The answer of The table displays the probabilities for each...

Question 13

The overnight shipping business has skyrocketed in the last ten years. The single greatest predictor of a companyʹs success is customer service. A study was conducted to determine the customer
Satisfaction levels for one overnight shipping business. In addition to the customerʹs satisfaction
Level, the customers were asked how often they used overnight shipping. The results are shown in
The following table: 
$\begin{array} { c | c c c | c } 
& \ { \text { Satisfaction level } } & \
\text { Frequency of Use } & \text { High } & \text { Medium } & \text { Low } & \text { TOTAL } \
\hline < 2 \text { per month } & 250 & 140 & 10 & 400 \
2 \text { - 5 per month } & 140 & 55 & 5 & 200 \
> 5 \text { per month } & 70 & 25 & 5 & 100 \
\hline \text { TOTAL } & 460 & 220 & 20 & 700
\end{array}$
Suppose that one customer who participated in the study is chosen at random. What is the probability that the customer had a low level of satisfaction and used the company two to five times per month?

Accepted Answer

The probability is calculated by dividing the number of customers who had a low level of satisfaction and used the company 2-5 times per month (5) by the total number of customers (700), resulting in $\frac{5}{700} = \frac{1}{140}$.

Question 14

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. Find $P ( A \cup B )$.

Accepted Answer

The answer of The table displays the probabilities for each...

Question 15

Unions and intersections cannot be defined for more than two sets, so that $A \cup B \cup C$ and $A \cap B \cap C$ are meaningless.

Accepted Answer

Unions and intersections can be defined for any number of sets, making expressions like $A \cup B \cup C$ and $A \cap B \cap C$ meaningful and valid for combining or finding common elements among three or more sets.

Question 16

Fill in the blank. The __________ of two events A and B is the event that either A or B or both occur.

Accepted Answer

The union of two events A and B includes all outcomes that are in A, in B, or in both A and B, which matches the description given.

Question 17

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.

Accepted Answer

The answer of A sample of 350 students was selected...

Question 18

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.  What is the probability that the restaurant is located in the northern portion of the United States?

Accepted Answer

The answer of A fast-food restaurant chain with 700 outlets...

Question 19

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 workerʹs political affiliation and type of job
Are noted.

Find the probability that the worker is a white collar worker affiliated with the Democratic Party.

Accepted Answer

The answer of The table shows the political affiliations and...

Question 20

Each manager of a Fortune 500 company was rated as being either a good, fair, or poor manager by his/her boss. The managerʹs educational background was also noted. The data appear below: 
$\begin{array}{l}
\text { Educational Background }\
\begin{array} { l | c c c c | c } 
\text { Manager } & & & & & \
\text { Rating } & \text { H. S. Degree } & \text { Some College } & \text { College Degree } & \text { Master's or Ph.D. } & \text { Total } \
\hline \text { Good } & 1 & 2 & 21 & 15 & 39 \
\text { Fair } & 3 & 19 & 43 & 22 & 87 \
\text { Poor } & 7 & 6 & 8 & 13 & 34 \
\hline \text { Total } & 11 & 27 & 72 & 50 & 160
\end{array}
\end{array}$
What is the probability that a randomly chosen manager has earned at least one college degree?

Accepted Answer

The probability that a randomly chosen manager has earned at least one college degree is calculated by adding the number of managers with a College Degree and those with a Master's or Ph.D., then dividing by the total number of managers. This gives $\frac{72 + 50}{160} = \frac{122}{160} = \frac{61}{80}$.

Quiz 3: Probability

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 3} B: {At least one of the dice shows a 2} True or False: $A \cup B = B$

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} True or False: $A \cap B = B .$

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?

Unions and intersections of events are examples of compound events.

Fill in the blank. The __________ of two events A and B is the event that both A and B occur.

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?

Unions and intersections cannot be defined for more than two sets, so that $A \cup B \cup C$ and $A \cap B \cap C$ are meaningless.

Fill in the blank. The __________ of two events A and B is the event that either A or B or both occur.

Quiz 3: Probability

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 3} B: {At least one of the dice shows a 2} True or False: A∪B=BA \cup B = BA∪B=B

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} True or False: A∩B=B.A \cap B = B .A∩B=B.

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?

Unions and intersections of events are examples of compound events.

Fill in the blank. The __________ of two events A and B is the event that both A and B occur.

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?

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 AAA be the event that the number rolled is less than 4 , and let BBB be the event that the number rolled is odd. Find P(A∩B) P ( A \cap B ) P(A∩B) .

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 AAA be the event that the number rolled is less than 4 , and let BBB be the event that the number rolled is odd. Find P(A∪B) P ( A \cup B ) P(A∪B) .

Unions and intersections cannot be defined for more than two sets, so that A∪B∪CA \cup B \cup CA∪B∪C and A∩B∩CA \cap B \cap CA∩B∩C are meaningless.

Fill in the blank. The __________ of two events A and B is the event that either A or B or both occur.

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 3} B: {At least one of the dice shows a 2} True or False: $A \cup B = B$

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} True or False: $A \cap B = B .$

Unions and intersections cannot be defined for more than two sets, so that $A \cup B \cup C$ and $A \cap B \cap C$ are meaningless.