Question 1

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:

Given that a manager is rated as fair, what is the probability that this manager has no college background?

Accepted Answer

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

Question 2

A researcher investigated whether a studentʹs seat preference was related in any way to the gender of the student. The researcher divided a lecture room into three sections (1-front, middle of the
Room, 2-front, sides of the classroom, and 3-back of the classroom, both middle and sides)and
Noted where each student sat on a particular day of the class. The researcherʹs summary table is
Provided below.

Suppose a person sitting in the front, middle portion of the class is randomly selected to answer a question. Find the probability that the person selected is female.

Accepted Answer

The answer of A researcher investigated whether a studentʹs seat...

Question 3

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
Probability that a green notepad is selected given that it is either blue or green.

Accepted Answer

Given the condition that the notepad is either blue or green, there are 6 blue and 6 green notepads, making a total of 12. The probability of selecting a green notepad from these is 6 out of 12, which simplifies to $\frac{1}{2}$.

Question 4

A local country club has a membership of 600 and operates facilities that include an 18-hole championship golf course and 12 tennis courts. Before deciding whether to accept new members,
The club president would like to know how many members regularly use each facility. A survey of
The membership indicates that 57% regularly use the golf course, 48% regularly use the tennis
Courts, and 9% use both of these facilities regularly. Given that a randomly selected member uses
The tennis courts regularly, find the probability that they also use the golf course regularly.

Accepted Answer

The answer of A local country club has a membership...

Question 5

For two events, $A$ and $B , P ( A ) = .4 , P ( B ) = .7$, and $P ( A \cap B ) = .2$. Find $P ( A \mid B )$.

Accepted Answer

$P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{.2}{.7} = .29$. This is the probability of event A given that event B has occurred.

Question 6

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
Probability that a yellow or pink notepad is selected given that it is either blue or green.

Accepted Answer

Given the condition that the notepad selected is either blue or green, the probability of selecting a yellow or pink notepad is 0, since these colors are not part of the condition.

Question 7

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?

Accepted Answer

The answer of Suppose that 80% of the employees of...

Question 8

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:

Given that an accident involved multiple vehicles, what is the probability that it involved alcohol?

Accepted Answer

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

Question 9

In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is earning
An A given that the student is a woman.

Accepted Answer

The probability that a student is earning an A given that the student is a woman is calculated using the formula for conditional probability: P(A|B) = P(A and B) / P(B). Here, A is the event of earning an A, and B is the event of being a woman. There are 7 women earning an A out of 22 women in total, so the probability is $\frac { 7 } { 22 }$.

Question 10

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.

Accepted Answer

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

Question 11

An economy pack of highlighters contains 12 yellow, 6 blue, 4 green, and 3 orange highlighters. An experiment consists of randomly selecting one of the highlighters and recording its color. Find
The probability that a blue or yellow highlighter is selected given that a yellow highlighter is
Selected.

Accepted Answer

Given that a yellow highlighter is selected, the probability of selecting a blue or yellow highlighter is 1, because the condition already satisfies the part of the event (selecting a yellow highlighter).

Question 12

In a class of 30 students, 18 are men, 6 are earning a B, and no men are earning a B. If a student is randomly selected from the class, find the probability that the student is a man given that the
Student earning a B.

Accepted Answer

Given that no men are earning a B, the probability of selecting a man given that the student is earning a B is 0, since all students earning a B are women.

Question 13

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?

Accepted Answer

The answer of A medium-sized company characterized their employees based...

Question 14

In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is a woman
Given that the student is earning an A.

Accepted Answer

The probability that a student is a woman given that the student is earning an A is calculated using the formula for conditional probability: P(A|B) = P(A and B) / P(B). Here, A is the event that a student is a woman, and B is the event that a student is earning an A. P(A and B) is the probability that a student is both a woman and earning an A, which is 7 out of the total 40 students, but since we're given that the student is earning an A, our total population for this calculation is the 10 students earning an A. Therefore, P(A|B) = 7/10.

Question 15

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.

Accepted Answer

The answer of Based on past experience, Josh believes that...

Question 16

For two events, $A$ and $B , P ( A ) = \frac { 1 } { 2 } , P ( B ) = \frac { 1 } { 3 }$, and $P ( A \cap B ) = \frac { 1 } { 4 }$. Find $P ( B \mid A )$.

Accepted Answer

The probability of $B$ given $A$ is calculated using the formula $P(B|A) = \frac{P(A \cap B)}{P(A)}$. Substituting the given values, we get $P(B|A) = \frac{1/4}{1/2} = \frac{1}{2}$.

Question 17

The manager of a used car lot took inventory of the automobiles on his lot and constructed the following table based on the age of each car and its make (foreign or domestic):

A car was randomly selected from the lot. Given that the car selected was a foreign car, what is the probability that it was older than 2 years old?

Accepted Answer

The answer of The manager of a used car lot...

Question 18

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.

Given that the worker is a Democrat, what is the probability that the worker has a white collar job.

Accepted Answer

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

Question 19

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 or received a merit raise?

Accepted Answer

The answer of Suppose that 62% of the employees at...

Question 20

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
Below in the following table:

A customer is chosen at random. Given that the customer uses the company two to five times per month, what is the probability that the customer expressed low satisfaction with the company?

Accepted Answer

The answer of The overnight shipping business has skyrocketed in...

Quiz 3: Probability

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 Probability that a green notepad is selected given that it is either blue or green.

For two events, $A$ and $B , P ( A ) = .4 , P ( B ) = .7$ , and $P ( A \cap B ) = .2$ . Find $P ( A \mid B )$ .

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 Probability that a yellow or pink notepad is selected given that it is either blue or green.

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?

In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is earning An A given that the student is a woman.

In a class of 30 students, 18 are men, 6 are earning a B, and no men are earning a B. If a student is randomly selected from the class, find the probability that the student is a man given that the Student earning a B.

In a class of 40 students, 22 are women, 10 are earning an A, and 7 are women that are earning an A. If a student is randomly selected from the class, find the probability that the student is a woman Given that the student is earning an A.

For two events, $A$ and $B , P ( A ) = \frac { 1 } { 2 } , P ( B ) = \frac { 1 } { 3 }$ , and $P ( A \cap B ) = \frac { 1 } { 4 }$ . Find $P ( B \mid A )$ .

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 or received a merit raise?