Question 1

Meagan Dubean manages a portfolio of 200 common stocks. Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.'  If a stock is selected randomly from Meagan's portfolio, P(Airlines|Income) = ___.

Accepted Answer

We are given that the portfolio stocks are classified by industry sector and investment objective. We are not given the exact numbers, but we know that there are at least some stocks in the Airlines industry sector and some stocks with an Income investment objective. 
Now, we need to find the probability of selecting a stock that is in the Airlines sector given that it has an Income investment objective. 
P(Airlines|Income) = P(Airlines and Income)/P(Income)
We are not given the exact numbers, so let's assume that there are 10 stocks in the Airlines sector and 50 stocks with an Income investment objective. We need to find out how many of those stocks fall into both categories. Let's say there are 4 stocks that are in both the Airlines sector and have an Income investment objective. 
P(Airlines and Income) = 4/200 = 0.02
P(Income) = 50/200 = 0.25
Now we can plug these values into the conditional probability equation: 
P(Airlines|Income) = 0.02/0.25 = 0.40
Therefore, the answer is B) 0.40.

Question 2

Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant. Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively. A plant employee is selected randomly; F is the event "works in the finishing department;" and A is the event "is absent excessively." P(A|F) = ___.

Accepted Answer

The answer of Abel Alonzo, Director of Human Resources, is...

Question 3

Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Find P(B|A).

Accepted Answer

The answer of Given P(A) = 0.45, P(B) = 0.30,...

Question 4

The marketing department of your company is investigating the appeal of three possible service plans your company is planning to offer. The table below gives information obtained through a sample of 2395 clients. The three service plans are labelled A, B, and C. The clients are classified according to their industry and their service plan preference.  If one of these consumers is randomly selected and prefers plan C, what is the probability that this client is from the construction industry?

Accepted Answer

The answer of The marketing department of your company is...

Question 5

The division of the company where you work has 85 employees. Thirty of them are bilingual, and 37% of the bilingual employees have a graduate degree. If an employee of this division is randomly selected, what is the probability that the employee is bilingual and has a graduate degree?

Accepted Answer

The answer of The division of the company where you...

Question 6

Define the following terms:
a) an experiment,
b) an event,
c) a sample space.

Accepted Answer

The answer of Define the following terms:
a) an experiment,
b) an...

Question 7

What are the three methods of assigning probabilities?

Accepted Answer

The answer of What are the three methods of assigning...

Question 8

A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labelled A, B, and C. The consumers are classified according to age and package design preference.  If one of these consumers is randomly selected and prefers design B, what is the probability that the person is 25 or older?

Accepted Answer

The answer of A market research firm is investigating the...

Question 9

The department in which you work in your company has 24 employees. A team of 3 employees must be selected to represent the department at a companywide meeting in the headquarters of the company. How many different teams of 3 can be selected?

Accepted Answer

The answer of The department in which you work in...

Question 10

A recently published study shows that 50% of Americans adults take multivitamins regularly. Another recent study showed that 20.6% of American adults work out regularly. Suppose that these two variables are independent. The probability that a randomly selected American adult takes multivitamins regularly and works out regularly is ___.

Accepted Answer

The answer of A recently published study shows that 50%...

Question 11

A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labelled A, B, and C. The consumers are classified according to age and package design preference. 
 Are "B" and "25 or older" independent and why or why $\textbf{        not? }$

Accepted Answer

The answer of A market research firm is investigating the...

Question 12

Name the branch of statistics that is supported by probability.

Accepted Answer

The answer of Name the branch of statistics that is...

Question 13

It is known that 20% of all students in some large university are overweight, 20% exercise regularly and 2% are overweight and exercise regularly. What is the probability that a randomly selected student is overweight given that this student exercises regularly?

Accepted Answer

The answer of It is known that 20% of all...

Question 14

Your company provides services to three different industries: automotive, construction, and financial services. These services can be either on a yearly or on a monthly contract. The cross-tabulation table below summarizes this information:  Suppose you know that a given client is a construction company and you are interested in the likelihood that this client is on a yearly contract. This is an example of ___.

Accepted Answer

This is an example of conditional probability because we are interested in the probability of a certain event (being on a yearly contract) given that we already know the client belongs to a certain industry (construction).

Question 15

The table below provides summary information about students in a class. The sex of each individual and their age range is given.  A student is randomly selected from this group, and it is found that the student is older than 25 years. What is the probability that the student is a male?

Accepted Answer

The answer of The table below provides summary information about...

Question 16

Max Sandlin is exploring the characteristics of stock market investors. He found that sixty percent of all investors have a net worth exceeding $1,000,000; 20% of all investors use an online brokerage; and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage. An investor is selected randomly, and E is the event "net worth exceeds $1, 000, 000," and O is the event "uses an online brokerage." P(O|E) = ___.

Accepted Answer

The answer of Max Sandlin is exploring the characteristics of...

Question 17

A market research firm is investigating the appeal of three package designs. The table below gives information obtained through a sample of 200 consumers. The three package designs are labelled A, B, and C. The consumers are classified according to age and package design preference.  If one of these consumers is randomly selected and is under 25, what is the probability that the person prefers design A?

Accepted Answer

The answer of A market research firm is investigating the...

Question 18

Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant. Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively. A plant employee is selected randomly; F is the event "works in the finishing department;" and A is the event "is absent excessively." P(F|A) = ___.

Accepted Answer

P(F|A) = P(F and A) / P(A) = 0.07 / 0.20 = 0.35.

Question 19

Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Which of the following is true?

Accepted Answer

If A and B were independent, then P(A and B) would be equal to P(A) × P(B) = 0.45 × 0.30 = 0.135. However, P(A and B) is given as 0.05, which is not equal to 0.135, so A and B are not independent. They are also not mutually exclusive because P(A and B) is not equal to 0. They are not collectively exhaustive or complementary either, as they do not cover all possibilities or add up to 1. Therefore, the only true statement is that A and B are not independent, so the answer is D.

Question 20

Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Find P(A|B).

Accepted Answer

We can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

Substituting the given values:

P(A|B) = 0.05 / 0.30

P(A|B) = 0.1667

Rounding to three decimal places, the answer is E) 0.167.

Quiz 5: Probability

Meagan Dubean manages a portfolio of 200 common stocks. Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' If a stock is selected randomly from Meagan's portfolio, P(Airlines|Income) = ___.

Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Find P(B|A) .

The division of the company where you work has 85 employees. Thirty of them are bilingual, and 37% of the bilingual employees have a graduate degree. If an employee of this division is randomly selected, what is the probability that the employee is bilingual and has a graduate degree?

Define the following terms: a) an experiment, b) an event, c) a sample space.

What are the three methods of assigning probabilities?

The department in which you work in your company has 24 employees. A team of 3 employees must be selected to represent the department at a companywide meeting in the headquarters of the company. How many different teams of 3 can be selected?

Name the branch of statistics that is supported by probability.

It is known that 20% of all students in some large university are overweight, 20% exercise regularly and 2% are overweight and exercise regularly. What is the probability that a randomly selected student is overweight given that this student exercises regularly?

The table below provides summary information about students in a class. The sex of each individual and their age range is given. A student is randomly selected from this group, and it is found that the student is older than 25 years. What is the probability that the student is a male?

Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Which of the following is true?

Given P(A) = 0.45, P(B) = 0.30, P(A and B) = 0.05. Find P(A|B) .