Question 1

In a recent article it was reported that 35.4% of all high school students smoke cigarettes.65% of these students plan on going to college.What is the probability that a randomly selected student smokes cigarettes and plans on going to college?

Accepted Answer

To find the probability that a randomly selected student smokes cigarettes and plans on going to college, we need to multiply the probabilities of both events.

Probability of smoking cigarettes = 35.4% = 0.354
Probability of planning to go to college = 65% = 0.65

P(smokes cigarettes and plans to go to college) = 0.354 x 0.65 = 0.230

Therefore, the best choice is B.

Question 2

An office of six people is plagued by high absenteeism.It is thought that the probability that an employee is absent on a particular day is 0.03.Assuming that the event that one person is absent on a particular day is independent of the absence of any other employee,what is the probability that at least one employee is absent tomorrow?

Accepted Answer

The probability of at least one employee being absent can be calculated using the complement rule as follows:

P(at least one absent) = 1 - P(no one absent)

P(no one absent) = (1-0.03)^6 = 0.8483

P(at least one absent) = 1-0.8483 = 0.1517 or approximately 0.167 (rounded to three decimal places)

Therefore, the best choice is D.

Question 3

If the firm interviewed was from the West,what is the probability that it expected medium or high growth?

Accepted Answer

First, we need to identify the total number of firms from the West, which is 20+15=35. 
Out of these 35 firms, the ones that expected medium or high growth are 12+10=22. 
Therefore, the probability of a firm from the West expecting medium or high growth is 22/35 or 0.46. 
Thus, the best choice is D.

Question 4

In a survey of 100 large corporations,it was found that 72% offer some form of tuition assistance plan for their workers.64% of the 100 corporations offer both a tuition assistance plan as well as provide dental insurance for dependents.What is the probability that a corporation that offers a tuition assistance plan also offers dental insurance for dependents?

Accepted Answer

The probability that a corporation offers dental insurance for dependents given that it offers a tuition assistance plan is calculated by dividing the number of corporations that offer both (64) by the number of corporations that offer a tuition assistance plan (72% of 100 = 72). So, the probability is 64/72 = 0.89.

Question 5

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A recent survey showed that 15% of computer programmers have experienced some form of wrist pain from typing,and that 25% are taking aspirin daily.Six percent of all programmers have both experienced some form of wrist pain from typing and taken aspirin on a daily basis.
-What is the probability that a programmer does not have wrist pain and does not take aspirin on a daily basis?

Accepted Answer

The probability of having wrist pain or taking aspirin is 0.15 + 0.25 - 0.06 = 0.34. Therefore, the probability of not having wrist pain and not taking aspirin is 1 - 0.34 = 0.66.

Question 6

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A survey of recent e-commerce start-up firms was undertaken at an industry convention.Representatives of the firm were asked for the geographic location of the firm as well as the firm's outlook for growth in the coming year.The results are provided below. 
-What is the probability that one of these start-up firms was from the Northeast?

Accepted Answer

The total number of firms surveyed is 200. The number of firms from the Northeast is 24. Therefore, the probability that a firm is from the Northeast is: 24/200 = 0.12. Therefore, choice B is correct.

Question 7

The purchasing agent for a municipality has contracted with a local car dealer to purchase four cars.The dealer has 25 cars on his lot;10 red,7 blue,6 white,and 2 purple.If the purchasing agent has no control over the colors he receives,what is the probability that he receives at least one of the purple cars?

Accepted Answer

The answer of The purchasing agent for a municipality has...

Question 8

Are the events "firm from the South" and "expects high growth" statistically independent?

Accepted Answer

The events are independent because the probability of a firm from the South expecting high growth is the same as the probability of a firm from the North expecting high growth.

Question 9

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A recent survey showed that 15% of computer programmers have experienced some form of wrist pain from typing,and that 25% are taking aspirin daily.Six percent of all programmers have both experienced some form of wrist pain from typing and taken aspirin on a daily basis.
-What is the probability that a programmer who takes aspirin on a daily basis has wrist pain?

Accepted Answer

P(wrist pain | aspirin) = P(wrist pain and aspirin) / P(aspirin)= 0.06 / 0.25= 0.24

Question 10

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A recent survey showed that 15% of computer programmers have experienced some form of wrist pain from typing,and that 25% are taking aspirin daily.Six percent of all programmers have both experienced some form of wrist pain from typing and taken aspirin on a daily basis.
-What is the probability that a programmer who has wrist pain takes aspirin on a daily basis?

Accepted Answer

The probability that a programmer who has wrist pain takes aspirin daily is found by dividing the percentage of programmers who have both experienced wrist pain and taken aspirin daily (6%) by the percentage of programmers who have experienced wrist pain (15%). This calculation gives 0.40 or 40%.

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 a vehicle navigation system given that he wants a better fuel efficiency is approximately:

Accepted Answer

The probability that a person wants a vehicle navigation system given that they want better fuel efficiency is found using the formula for conditional probability: P(A|B) = P(A and B) / P(B). Here, A is the event of wanting a vehicle navigation system, and B is the event of wanting better fuel efficiency. Given that 45% want both features and 80% want better fuel efficiency, P(A|B) = 0.45 / 0.80 = 0.5625, which is approximately 0.56.

Question 12

As the office manager for a medical office with ten doctors,you are responsible for developing the roster for the on-call shift for the next three nights.How many different ways could you assign a different doctor to each of the next three nights?

Accepted Answer

For the first night, we can choose any of the ten doctors. 
For the second night, we can choose any of the remaining nine doctors. 
For the third night, we can choose any of the remaining eight doctors.

Therefore, the total number of ways to assign a different doctor to each of the next three nights is:

10 x 9 x 8 = 720.

Thus, the best choice is C).

Question 13

Which of the following statements is true?

Accepted Answer

If events A and B are mutually exclusive, then they cannot occur together. Hence, the intersection of A and B is the empty set.

Question 14

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Given A= {ES1U1B13S1U1B0,ES1U1B14S1U1B0,ES1U1B18S1U1B0,ES1U1B110S1U1B0} and B = {ES1U1B13S1U1B0,ES1U1B14S1U1B0,ES1U1B16S1U1B0,ES1U1B19S1U1B0}
-What is the intersection of A and B?

Accepted Answer

The intersection of A and B is the set of elements that are common to both sets A and B. Only E₃ and E₄ are present in both sets, hence the answer is A.

Question 15

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Given A= {ES1U1B13S1U1B0,ES1U1B14S1U1B0,ES1U1B18S1U1B0,ES1U1B110S1U1B0} and B = {ES1U1B13S1U1B0,ES1U1B14S1U1B0,ES1U1B16S1U1B0,ES1U1B19S1U1B0}
-What is the union of A and B?

Accepted Answer

The union of A and B is the set of all elements in A and all elements in B, with duplicates removed. Therefore, the union of A and B is {E₃, E₄, E₆, E₈, E₉, E₁₀}.

Question 16

A junior executive looking at his business attire in his closet notes that he has eight suits,six shirts,and four 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

The number of combinations for choosing 2 suits from 8 is 28, for choosing 2 shirts from 6 is 15, and for choosing 2 pairs of shoes from 4 is 6. Multiply these together: 28 * 15 * 6 = 2520.

Question 17

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A recent survey showed that 15% of computer programmers have experienced some form of wrist pain from typing,and that 25% are taking aspirin daily.Six percent of all programmers have both experienced some form of wrist pain from typing and taken aspirin on a daily basis.
-What is the probability that a programmer has wrist pain and does not take aspirin on a daily basis?

Accepted Answer

The probability of having wrist pain is 0.15. The probability of having both wrist pain and taking aspirin is 0.06. Therefore, the probability of having wrist pain and not taking aspirin is 0.15 - 0.06 = 0.09.

Question 18

A gumball machine has six red gumballs,four blue gumballs,and three yellow gumballs.If you buy three gumballs,what is the probability that you get three different colors?

Accepted Answer

The probability of getting three gumballs of different colors can be calculated by considering the total ways to pick one gumball of each color divided by the total ways to pick any three gumballs. The total ways to pick one gumball of each color is simply the product of the number of gumballs of each color, which is 6 (red) * 4 (blue) * 3 (yellow) = 72 ways. The total ways to pick any three gumballs from the 13 available (6 red + 4 blue + 3 yellow = 13) is calculated using combinations (since the order of selection does not matter), which is 13 choose 3 = 13! / (3!(13-3)!) = 286 ways. Therefore, the probability is 72 / 286 = 0.252.

Question 19

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
A recent survey showed that 15% of computer programmers have experienced some form of wrist pain from typing,and that 25% are taking aspirin daily.Six percent of all programmers have both experienced some form of wrist pain from typing and taken aspirin on a daily basis.
-What is the probability that a programmer has wrist pain or takes aspirin on a daily basis?

Accepted Answer

To find the probability that a programmer has wrist pain or takes aspirin on a daily basis, we need to add the probabilities of each event and subtract the probability of both happening together. 
P(Wrist pain or Takes aspirin) = P(Wrist pain) + P(Takes aspirin) - P(Wrist pain and Takes aspirin) 
= 0.15 + 0.25 - 0.06 
= 0.34. 
Therefore, the correct answer is choice C (0.34).

Question 20

If the firm interviewed was expecting medium or high growth,what is the probability of the firm being located in the West?

Accepted Answer

From the contingency table, we can see that there are a total of 395+204+236=835 firms that are expecting medium or high growth. Out of these, 204 are located in the West. Therefore, the probability of the firm being located in the West given that it is expecting medium or high growth is 204/835, which simplifies to 0.244 or 0.31 when rounded to two decimal places. The closest option is B, 0.31, so that is the answer.

Quiz 3: Probability

In a recent article it was reported that 35.4% of all high school students smoke cigarettes.65% of these students plan on going to college.What is the probability that a randomly selected student smokes cigarettes and plans on going to college?

If the firm interviewed was from the West,what is the probability that it expected medium or high growth?

Are the events "firm from the South" and "expects high growth" statistically independent?

As the office manager for a medical office with ten doctors,you are responsible for developing the roster for the on-call shift for the next three nights.How many different ways could you assign a different doctor to each of the next three nights?

Which of the following statements is true?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Given A= {E₃,E₄,E₈,E₁₀} and B = {E₃,E₄,E₆,E₉} -What is the intersection of A and B?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Given A= {E₃,E₄,E₈,E₁₀} and B = {E₃,E₄,E₆,E₉} -What is the union of A and B?

A junior executive looking at his business attire in his closet notes that he has eight suits,six shirts,and four 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?

A gumball machine has six red gumballs,four blue gumballs,and three yellow gumballs.If you buy three gumballs,what is the probability that you get three different colors?

If the firm interviewed was expecting medium or high growth,what is the probability of the firm being located in the West?

Quiz 3: Probability

In a recent article it was reported that 35.4% of all high school students smoke cigarettes.65% of these students plan on going to college.What is the probability that a randomly selected student smokes cigarettes and plans on going to college?

If the firm interviewed was from the West,what is the probability that it expected medium or high growth?

Are the events "firm from the South" and "expects high growth" statistically independent?

As the office manager for a medical office with ten doctors,you are responsible for developing the roster for the on-call shift for the next three nights.How many different ways could you assign a different doctor to each of the next three nights?

Which of the following statements is true?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Given A= {E3,E4,E8,E10} and B = {E3,E4,E6,E9} -What is the intersection of A and B?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Given A= {E3,E4,E8,E10} and B = {E3,E4,E6,E9} -What is the union of A and B?

A junior executive looking at his business attire in his closet notes that he has eight suits,six shirts,and four 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?

A gumball machine has six red gumballs,four blue gumballs,and three yellow gumballs.If you buy three gumballs,what is the probability that you get three different colors?

If the firm interviewed was expecting medium or high growth,what is the probability of the firm being located in the West?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Given A= {E₃,E₄,E₈,E₁₀} and B = {E₃,E₄,E₆,E₉} -What is the intersection of A and B?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Given A= {E₃,E₄,E₈,E₁₀} and B = {E₃,E₄,E₆,E₉} -What is the union of A and B?