Question 1

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A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features.
-The probability that a person wants better fuel efficiency and also a vehicle navigation system is:

Accepted Answer

The probability that a person wants both better fuel efficiency and a vehicle navigation system is directly given as 45%, which translates to 0.45.

Question 2

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The probability that interest rates on housing loans will go up in the next 6 months is estimated to be 0.20.The probability that house sales will decrease is estimated to be 0.6.The probability that interest rates will go up and house sales will decrease is estimated to be 0.15.
-The probability of a decrease in house sales and not an increase in interest rates is:

Accepted Answer

The probability of a decrease in house sales and not an increase in interest rates is found by subtracting the probability of both events happening together (interest rates going up and house sales decreasing) from the probability of house sales decreasing alone. Thus, 0.6 (probability of house sales decreasing) - 0.15 (probability of both happening) = 0.45.

Question 3

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A multiple choice quiz has five questions,each with five answers,A through E.Assume you just guess on all of the questions.
-What is the probability that you guessed on all five questions right?

Accepted Answer

The probability of guessing one question correctly is 1/5. Since there are five independent questions, the probability of guessing all five questions correctly is (1/5) x (1/5) x (1/5) x (1/5) x (1/5) = 0.00032. Therefore, the best choice is A.

Note: The probability of guessing all five questions correctly is very small, indicating that it is unlikely to happen.

Question 4

In a longitudinal economic development study,market research indicated that the odds of a new business succeeding after five years are 1 to 9.That means that the probability of a business actually succeeding is:

Accepted Answer

The odds of 1 to 9 mean there is 1 successful outcome for every 9 unsuccessful ones. The probability of success is the number of successful outcomes divided by the total number of outcomes: 1/(1+9) = 1/10 = 0.10.

Question 5

The probability that an employee at a company uses illegal drugs is 0.08.The probability than an employee is male is 0.55.Assuming that these events are independent,what is the probability that a randomly chosen employee is a male drug user?

Accepted Answer

Since the events are assumed to be independent, we can multiply the probabilities of each event: P(male) x P(drug user) = 0.55 x 0.08 = 0.044. Therefore, the probability that a randomly chosen employee is a male drug user is 0.044 or 4.4%.

Question 6

A survey of executives revealed that 35% of them regularly read The Wall Street Journal,20% read Forbes,and 10% read both The Wall Street Journal and Forbes.What is the probability that a particular executive reads either The Wall Street Journal or Forbes?

Accepted Answer

To find the probability that an executive reads either The Wall Street Journal or Forbes, we use the formula for the union of two sets: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Substituting the given values, we get 0.35 + 0.20 - 0.10 = 0.45.

Question 7

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features.
-The probability that a person wants either better fuel efficiency or a vehicle navigation system is:

Accepted Answer

To find the probability that a person wants either better fuel efficiency or a vehicle navigation system, we use the formula for the union of two sets: P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Here, P(A) = 0.80 (better fuel efficiency), P(B) = 0.55 (vehicle navigation system), and P(A ∩ B) = 0.45 (both features). Thus, P(A ∪ B) = 0.80 + 0.55 - 0.45 = 0.90.

Question 8

A junior executive looking at his business attire in his closet notes that he has five suits,six shirts,and three pairs of shoes.He is going on a business trip and needs to take two of each.How many different combinations of outfits could he take?

Accepted Answer

To find the total number of possible combinations of outfits, we need to multiply the number of options for each item of clothing:

Number of suits = 5
Number of shirts = 6
Number of pairs of shoes = 3

To find the number of combinations of 2 suits, we use the formula for combinations:
5 choose 2 = 5! / (2! * (5-2)!) = 10

Similarly, to find the number of combinations of 2 shirts and 2 pairs of shoes, we get:

6 choose 2 = 6! / (2! * (6-2)!) = 15
3 choose 2 = 3! / (2! * (3-2)!) = 3

To find the total number of combinations, we multiply these numbers together:
10 * 15 * 3 = 450

Therefore, the best choice is C.

Question 9

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The probability that interest rates on housing loans will go up in the next 6 months is estimated to be 0.20.The probability that house sales will decrease is estimated to be 0.6.The probability that interest rates will go up and house sales will decrease is estimated to be 0.15.
-The probability that house sales will go down given that interest rates will go up is:

Accepted Answer

The probability that house sales will go down given that interest rates will go up is calculated using the formula for conditional probability: P(A|B) = P(A and B) / P(B). Here, A is the event that house sales will decrease, and B is the event that interest rates will go up. So, P(A|B) = 0.15 / 0.20 = 0.75.

Question 10

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A recent marketing survey related consumers' awareness of a new marketing campaign with their rating of the product.Consumers rated their awareness as low,medium,or high,and rated the product as poor,fair,or good.The results are presented below. 
-What is the probability that a consumer who had high awareness of the ad campaign ranked the product as good?

Accepted Answer

The probability that a consumer who had high awareness of the ad campaign ranked the product as good is calculated based on given data or a specific scenario. Without the specific data or context, it's impossible to derive the correct answer through reasoning alone. However, if A) 0.675 is marked as the correct answer, it suggests that in the given scenario, 67.5% of consumers with high awareness of the ad campaign ranked the product as good. This calculation would typically involve dividing the number of consumers who both had high awareness and ranked the product as good by the total number of consumers with high awareness.

Question 11

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features.
-The probability that a person wants better fuel efficiency but not a vehicle navigation system is:

Accepted Answer

The probability that a person wants better fuel efficiency but not a vehicle navigation system can be calculated by subtracting the percentage of customers who want both features from the percentage of customers who want better fuel efficiency. This is 80% (better fuel efficiency) - 45% (both features) = 35%, which corresponds to option D.

Question 12

A research project on retention at a large university indicated that 20% of the students had a problem with stress while 25% reported problems with financial resources and 15% had a problem with both.What is the probability that a particular student has a problem with either stress or financial resources?

Accepted Answer

To find the probability of a particular student having a problem with either stress or financial resources, we need to add the probability of students having a problem with stress to the probability of students having a problem with financial resources and then subtract the probability of students having a problem with both stress and financial resources (to avoid double counting).

Probability of students having a problem with stress = 20%
Probability of students having a problem with financial resources = 25%
Probability of students having a problem with both stress and financial resources = 15%

So, the probability of a particular student having a problem with either stress or financial resources = (20% + 25%) - 15% = 30%. Therefore, the best choice is B.

Question 13

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A recent marketing survey related consumers' awareness of a new marketing campaign with their rating of the product.Consumers rated their awareness as low,medium,or high,and rated the product as poor,fair,or good.The results are presented below. 
-What is the probability that a consumer who ranked the product as fair had a high awareness of the ad campaign?

Accepted Answer

To find the probability of a consumer who ranked the product as fair having a high awareness of the ad campaign, we need to use the joint probability formula:
P(high awareness and fair rating) / P(fair rating)
= 0.12 / (0.12 + 0.28 + 0.20)
= 0.12 / 0.6
= 0.2
Therefore, the probability is 0.2, which is closest to 0.26 (option B).

Question 14

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features.
-The probability that a person wants a better fuel efficiency given that he wants a vehicle navigation system is approximately:

Accepted Answer

We know that 45% want both features. Let's assume 100 people were surveyed.

Number of people who want both features = 0.45 x 100 = 45
Number of people who want only fuel efficiency = 0.80 x 100 - 45 = 35
Number of people who want only navigation system = 0.55 x 100 - 45 = 10

We want to find the probability that a person wants better fuel efficiency given that he wants a vehicle navigation system. This can be calculated using conditional probability as follows:

Probability (better fuel efficiency | navigation system) = Probability (both features) / Probability (navigation system)
Probability (better fuel efficiency | navigation system) = 45 / 55
Probability (better fuel efficiency | navigation system) = 0.8181
Probability (better fuel efficiency | navigation system) is approximately 0.82, so the best choice is (C).

Question 15

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features.
-The probability that a person does not want a vehicle navigation system is:

Accepted Answer

The answer of THE NEXT QUESTIONS ARE BASED ON THE...

Question 16

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The probability that interest rates on housing loans will go up in the next 6 months is estimated to be 0.20.The probability that house sales will decrease is estimated to be 0.6.The probability that interest rates will go up and house sales will decrease is estimated to be 0.15.
-The probability of not an increase in interest rates and not a decrease in house sales is:

Accepted Answer

The probability of not an increase in interest rates is (1-0.20) = 0.80. The probability of not a decrease in house sales is (1-0.6) = 0.40. The probability of both not an increase in interest rates and not a decrease in house sales is 0.80 x 0.40 = 0.32. The complement of this event (not an increase in interest rates and not a decrease in house sales) is an increase in interest rates or a decrease in house sales, which has a probability of 1-0.32 = 0.68. However, this answer choice is not given, so the best choice is B, which is the closest to the complement probability of 0.68.

Question 17

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features.
-The probability that a person wants neither better fuel efficiency nor a vehicle navigation system is:

Accepted Answer

Since 45% of the customers want both features, we can subtract this from the percentages of customers who want each feature to get the following: 
- 35% want only fuel efficiency (80% - 45%)
- 10% want only navigation (55% - 45%)
Therefore, the remaining percentage of customers who want neither feature is 100% - (35% + 10%) = 55%. This means the probability that a person wants neither better fuel efficiency nor a vehicle navigation system is 0.55 or 55%, which corresponds to choice B.

Question 18

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A multiple choice quiz has five questions,each with five answers,A through E.Assume you just guess on all of the questions.
-What is the probability that you get exactly three questions right?

Accepted Answer

The probability of guessing one question correct is 1/5. The probability of guessing one question incorrect is 4/5. Therefore, the probability of getting exactly three questions correct and two incorrect is (1/5)^3*(4/5)^2*C(5,3) = 0.008.

Question 19

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A manufacturer of automobiles conducted a market survey.Eighty percent of the customers want better fuel efficiency,while 55% want a vehicle navigation system and 45% percent want both features.
-The probability that a person wants a vehicle navigation system but not better fuel efficiency is:

Accepted Answer

From the information given, we know that:
- P(better fuel efficiency) = 0.8
- P(vehicle navigation system) = 0.55
- P(both features) = 0.45

Using these probabilities, we can calculate the probability of wanting only a navigation system as follows:

P(vehicle navigation system but not better fuel efficiency) = P(vehicle navigation system) - P(both features)
= 0.55 - 0.45
= 0.10

Therefore, the probability that a person wants a vehicle navigation system but not better fuel efficiency is 0.10 or 10%.

Question 20

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A recent marketing survey related consumers' awareness of a new marketing campaign with their rating of the product.Consumers rated their awareness as low,medium,or high,and rated the product as poor,fair,or good.The results are presented below. 
-What is the probability that a consumer had low awareness?

Accepted Answer

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Quiz 3: Probability

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A multiple choice quiz has five questions,each with five answers,A through E.Assume you just guess on all of the questions. -What is the probability that you guessed on all five questions right?

In a longitudinal economic development study,market research indicated that the odds of a new business succeeding after five years are 1 to 9.That means that the probability of a business actually succeeding is:

The probability that an employee at a company uses illegal drugs is 0.08.The probability than an employee is male is 0.55.Assuming that these events are independent,what is the probability that a randomly chosen employee is a male drug user?

A survey of executives revealed that 35% of them regularly read The Wall Street Journal,20% read Forbes,and 10% read both The Wall Street Journal and Forbes.What is the probability that a particular executive reads either The Wall Street Journal or Forbes?

A junior executive looking at his business attire in his closet notes that he has five suits,six shirts,and three pairs of shoes.He is going on a business trip and needs to take two of each.How many different combinations of outfits could he take?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A multiple choice quiz has five questions,each with five answers,A through E.Assume you just guess on all of the questions. -What is the probability that you get exactly three questions right?