Question 1

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.'  Which of the following statements is not true?
A)Growth and Income are complementary events.
B)Electronics and Growth are dependent.
C)Electronics and Healthcare are mutually exclusive.
D)Airlines and Healthcare are collectively exhaustive.
E)Growth and Income are collectively exhaustive.

Accepted Answer

The answer of Meagan Dubean manages a portfolio of 200...

Question 2

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.The complement of F is ___________.
A){Albert,Betty,Jack,Patty}
B){Betty,Patty,Meagan}
C){Albert,Abel,Jack}
D){Betty,Abel}
E){Meagan}

Accepted Answer

The complement of F includes all elements in S that are not in F. Thus, it is {Albert, Abel, Jack}

Question 3

Which of the following is not a legitimate probability value?
A)0.87
B)12/13
C)0.05
D)5/4
E)0.93

Accepted Answer

A legitimate probability value must be between 0 and 1, inclusive. Choice D is greater than 1, so it is not a legitimate probability value.

Question 4

Let F be the event that a student is enrolled in afinance course,and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.Find the probability that a student is in finance and is also in statistics.
A)0.15
B)0.70
C)0.55
D)0.12
E)0.60

Accepted Answer

The answer of Let F be the event that a...

Question 5

Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.A student is randomly selected,what is the probability that the student is enrolled in either finance or statistics or both?
A)0.15
B)0.75
C)0.60
D)0.55
E)0.90

Accepted Answer

We can use the formula:
P(F or S) = P(F) + P(S) - P(F and S)
P(F or S) = 0.40 + 0.35 - 0.15
P(F or S) = 0.60

Question 6

In a set of 12 aluminum castings,two castings are defective (D),and the remaining ten are good (G).A quality control inspector randomly selects three of the twelve castings with replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains __________ elementary events.
A)1,728
B)220
C)120
D)10
E)66

Accepted Answer

The answer of In a set of 12 aluminum castings,two...

Question 7

Which of the following statements is not true regarding probabilities: 
A)probability is the basis for inferential statistics
B)probabilities are subjective measures with limited value in business.
C)probabilities are used to determine the likelihood of certain outcomes
D)probabilities can inform many business decisions.

Accepted Answer

Probabilities are objective measures that can provide valuable insights for making informed and rational business decisions. While probabilities involve some degree of uncertainty, they are based on mathematical principles and objective data, not subjective opinions. Therefore, option B is not true.

Question 8

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.'  Which of the following statements is true?
A)Growth and Healthcare are complementary events.
B)Electronics and Growth are independent.
C)Electronics and Growth are mutually exclusive.
D)Airlines and Healthcare are collectively exhaustive.
E)Electronics and Healthcare are collectively exhaustive.

Accepted Answer

The statement "Electronics and Growth are independent" means that the performance of electronics stocks does not affect the performance of growth stocks, and vice versa. This is a true statement, as the two categories are not directly related to each other. The other options are not true, as they either suggest a relationship between the two categories or use terms (such as "collectively exhaustive") that do not apply to this situation.

Question 9

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method
A)subjective probability
B)relative frequency
C)classical probability
D)a priori probability
E)a posterior probability

Accepted Answer

The method of assigning probability based on the classical probability assumes that all outcomes are equally likely. In a deck of cards, there are 52 cards and only one ace of spades, so the probability of drawing the ace of spades is 1/52. This is an example of classical probability.

Question 10

In a set of 25 aluminum castings,four castings are defective (D),and the remaining twenty-one are good (G).A quality control inspector randomly selects three of the twenty-five castings without replacement,and classifies each as defective (D)or good (G).The sample space for this experiment contains ____________ elementary events.
A)12,650
B)2,300
C)455
D)16
E)15,6255

Accepted Answer

The answer of In a set of 25 aluminum castings,four...

Question 11

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience,she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.
A)subjective probability
B)relative frequency
C)classical probability
D)a priori probability
E)a posterior probability

Accepted Answer

The scenario describes Belinda's personal opinion based on her experience, indicating a subjective assessment of probability. Therefore, the method of assigning probabilities used here is subjective probability.

Question 12

Which of the following statements in not true? 
A)the marginal probability uses the total possible outcomes in the denominator
B)the union probability is the probability of X or Y occurring.
C)the joint probability uses the probability of X in the denominator
D)the conditional probability uses subtotal of the possible outcomes in denominator

Accepted Answer

The joint probability uses the total possible outcomes in the denominator, not the probability of X.

Question 13

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.F $\cup$ H is ___________.
A){Meagan}
B){Betty,Abel,Patty,Meagan}
C)empty,since F and H are complements
D)empty,since F and H are independent
E)empty,since F and H are mutually exclusive

Accepted Answer

The answer of Consider the following sample space,S,and several events...

Question 14

If E and F are mutually exclusive,then _______.
A)the probability of the union is zero
B)P(E)= 1 - P(F)
C)the probability of the intersection is zero
D)the probability of the union is one
E)P(E)= P(F)

Accepted Answer

Mutually exclusive events cannot occur at the same time, so their intersection is empty (i.e., has a probability of zero).

Question 15

Which of the following is a legitimate probability value?
A)1.67
B)16/15
C)-0.23
D)3/2
E)0.28

Accepted Answer

A probability value must be a non-negative number between 0 and 1, inclusive. Option E, 0.28, satisfies this criteria.

Question 16

The list of all elementary events for an experiment is called _______.
A)the sample space
B)the exhaustive list
C)the population space
D)the event union
E)a frame

Accepted Answer

The list of all elementary events for an experiment is called the sample space.

Question 17

The number of different committees of 2 students that can be chosen from a group of 5 students is
A)20
B)2
C)5
D)10
E)1

Accepted Answer

The number of different committees of 2 students that can be chosen from a group of 5 students can be found using the combination formula, which is C(5,2) or 5 choose 2. This is equal to 5!/[(5-2)!2!] = 10, which means there are 10 different committees of 2 students that can be chosen from the group of 5 students. Therefore, the answer is D)10.

Question 18

Let F be the event that a student is enrolled in a finance course,and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in an finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.Find P(S).
A)0.15
B)0.35
C)0.40
D)0.55
E)0.60

Accepted Answer

We can use the formula: P(S) = P(S and F') + P(S and F) where F' represents not enrolled in finance.

We know that P(F) = 0.4 and P(S) = 0.35, and 15% are enrolled in both. So, P(F and S) = 0.15.

Substituting into the formula, we get:
P(S) = P(S and F') + P(S and F)
P(S) = P(not enrolled in finance and enrolled in statistics) + P(enrolled in finance and enrolled in statistics)
P(S) = 0.35 - 0.15 + 0.15
P(S) = 0.35

Therefore, the answer is B) 0.35.

Question 19

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.F $\cap$ H is ___________.
A){Meagan}
B){Betty,Patty,Abel,Meagan}
C)empty,since F and H are complements
D)empty,since F and H are independent
E)empty,since F and H are mutually exclusive

Accepted Answer

The intersection of F and H, denoted as F ∩ H, is the set of elements that are common to both F and H. In this case, F = {Betty, Patty, Meagan} and H = {Abel, Meagan}. The only common element between F and H is Meagan, so F ∩ H = {Meagan}.

Question 20

If X and Y are mutually exclusive events,then if X occurs _______.
A)Y must also occur
B)Y cannot occur
C)X and Y are independent
D)X and Y are complements
E)A and Y are collectively exhaustive

Accepted Answer

If X and Y are mutually exclusive events, it means they cannot occur at the same time. Therefore, if X occurs, Y cannot occur.

Quiz 4: Probability

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' Which of the following statements is not true?

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.The complement of F is ___________.

Which of the following is not a legitimate probability value?

Which of the following statements is not true regarding probabilities:

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' Which of the following statements is true?

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience,she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.

Which of the following statements in not true?

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.F ∪\cup∪ H is ___________.

If E and F are mutually exclusive,then _______.

Which of the following is a legitimate probability value?

The list of all elementary events for an experiment is called _______.

The number of different committees of 2 students that can be chosen from a group of 5 students is

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.F ∩\cap∩ H is ___________.

If X and Y are mutually exclusive events,then if X occurs _______.

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.F $\cup$ H is ___________.

Consider the following sample space,S,and several events defined on it.S = {Albert,Betty,Abel,Jack,Patty,Meagan},and the events are: F = {Betty,Patty,Meagan},H = {Abel,Meagan},and P = {Betty,Abel}.F $\cap$ H is ___________.