Question 1

Events are collectively exhaustive if _____________.
A) they include all events.
B) they are included in all events.
C) they contain all outcomes of an experiment.
D) they do not share any common outcomes of an experiment.

Accepted Answer

Events are collectively exhaustive if they contain all possible outcomes of an experiment, meaning no other outcome is possible outside of those events.

Question 2

In an experiment in which a coin is tossed twice,which of the following represents mutually exclusive and collectively exhaustive events?
A) {TT,HH} and {TT,HT}
B) {HT,TH} and {HH,TH}
C) {TT,HH} and {TH,HT}
D) {TT,HT} and {HT,TH}

Accepted Answer

The events in choice C are mutually exclusive because they do not share any outcomes (TT and HH vs. TH and HT), and they are collectively exhaustive because they include all possible outcomes of a two-coin toss. Choices A, B, and D are not collectively exhaustive because they do not include all possible outcomes.

Question 3

Mutually exclusive and collectively exhaustive events ______________.
A) contain all outcomes in a sample space and may share common outcomes.
B) contain all outcomes in a sample space and do not share common outcomes.
C) do not have to contain all outcomes in a sample space but do not share common outcomes.
D) do not have to contain all outcomes in a sample space and may share common outcomes.

Accepted Answer

Mutually exclusive events do not share common outcomes, while collectively exhaustive events contain all outcomes in a sample space. Therefore, if two events are both mutually exclusive and collectively exhaustive, they must contain all outcomes in a sample space and not share common outcomes, making B the correct choice.

Question 4

A sample space contains _________________.
A) outcomes of the relevant events.
B) several outcomes of an experiment.
C) all possible outcomes of an experiment.
D) one of several outcomes of an experiment.

Accepted Answer

A sample space contains all possible outcomes of an experiment. Option A only refers to some outcomes, option B refers to several outcomes but not necessarily all, and option D implies a limited number of outcomes which is not necessarily the case.

Question 5

For the sample space S = {apple pie,cherry pie,peach pie,pumpkin pie},what is the complement of A = {pumpkin pie,cherry pie}?
A) {apple pie}
B) {peach pie}
C) {apple pie,peach pie}
D) {pumpkin pie,cherry pie}

Accepted Answer

The complement of A would be all the pies in the sample space that are not pumpkin pie or cherry pie. Therefore, apple pie and peach pie are the only pies left in the sample space, making the answer choice C the correct complement.

Question 6

If A and B are _______ ________ events,then the addition rule is defined as

Accepted Answer

The answer of If A and B are _______ ________...

Question 7

Events are considered _________ if the occurrence of one is related to the probability of the occurrence of the other.

Accepted Answer

The answer of Events are considered _________ if the occurrence...

Question 8

What is a simple event?
A) An event that contains all outcomes of a sample space
B) An event that contains several outcomes of a sample space
C) An event that contains only one outcome of a sample space
D) All of the above

Accepted Answer

A simple event is an event that contains only one outcome of a sample space. Therefore, the best answer is C. A is incorrect because it refers to the entire sample space, which is not a simple event. B is incorrect because it refers to an event that contains multiple outcomes, which is not a simple event.

Question 9

Which of the following represents a subjective probability?
A) The probability of rolling a 2 on a single die is one in six.
B) Based on a conducted experiment,the probability of tossing a head on an unfair coin is 0.6.
C) A skier believes she has a 10% chance of winning a gold medal.
D) Based on past observation,a manager believes there is a three-in-five chance of retaining an employee for at least one year.

Accepted Answer

Subjective probability is based on personal judgment or opinion rather than on precise calculation or empirical evidence. Choice C, where a skier believes she has a 10% chance of winning a gold medal, is an example of subjective probability because it is based on the skier's personal belief rather than objective data.

Question 10

A probability based on logical analysis rather than on observation or personal judgment is best referred to as a(n)_______________.
A) a priori probability.
B) empirical probability.
C) subjective probability.
D) None of the above.

Accepted Answer

A probability based on logical analysis rather than on observation or personal judgment is known as a priori probability. This type of probability is based on reasoning and deductive logic, rather than on empirical data or subjective opinions. Examples include theoretical probabilities calculated in mathematical models or probabilities determined through logical analysis of a situation or event. Empirical probability is based on observation or data, while subjective probability is based on personal judgment or beliefs.

Question 11

An analyst has a limit order outstanding on a stock.He argues that the probability that the order will execute before the close of trading is 0.20.Thus,the odds for the order executing before the close of trading are
A) one in four.
B) one in five.
C) four to one.
D) five to one.

Accepted Answer

The answer of An analyst has a limit order outstanding...

Question 12

Which of the following are mutually exclusive events of an experiment in which two coins are tossed?
A) {TT,HH} and {TT}
B) {HT,TH} and {TH}
C) {TT,HT} and (HT}
D) (TT,HH} and {TH}

Accepted Answer

The answer of Which of the following are mutually exclusive...

Question 13

For an experiment in which a single die is rolled,the sample space is __________.
A) {1,1,3,4,5,6}.
B) {2,1,3,6,5,4}.
C) {1,2,3,4,4,5}.
D) All of the above

Accepted Answer

The sample space for rolling a single die is {1, 2, 3, 4, 5, 6}. Option B contains all the possible outcomes in a random order. Options A and C have repeated values, which are not possible outcomes for rolling a single die. Option D is incorrect because not all options contain the correct sample space.

Question 14

An analyst believes the probability that U.S.stock returns exceed long-term corporate bond returns over a five-year period is based on personal assessment.This type of probability is best characterized as a(n)___________.
A) a priori probability.
B) empirical probability.
C) objective probability.
D) subjective probability.

Accepted Answer

Subjective probability is based on personal assessment or judgement, as opposed to objective or empirical probability, which is based on actual observed data. A priori probability is based on mathematical calculations or logical deductions, which is not applicable in this scenario.

Question 15

Assume the sample space S = {win,loss}.Select the choice that fulfills the requirements of the definition of probability.
A) P({win})= 0.7,P({loss})= 0.2
B) P({win})= 0.7,P({loss})= 0.3
C) P({win})= 1.0,P({loss})= 0.1
D) P({win})= 0.5,P({loss})= -0.5

Accepted Answer

The probabilities for each outcome must be between 0 and 1, and they must add up to 1. Option B satisfies these requirements, with P({win})=0.7 and P({loss})=0.3, adding up to 1. Options A and C also satisfy these requirements, but option B has the highest probability of winning, making it the best choice. Option D is not valid because the probability for the loss outcome is negative.

Question 16

Mutually exclusive events _____________.
A) contain all possible outcomes.
B) may share common outcomes.
C) do not share common outcomes.
D) do not contain all possible outcomes.

Accepted Answer

Mutually exclusive events do not share common outcomes.

Question 17

Which of the following represents an empirical probability?
A) The probability of tossing a head on a coin is 0.5.
B) The probability of rolling a 2 on a single die is one in six.
C) A skier believes she has a 0.10 chance of winning a gold medal.
D) Based on past observation,a manager believes there is a three-in-five chance of retaining an employee for at least one year.

Accepted Answer

Empirical probability is based on observed data rather than theoretical calculations. Option D is an example of empirical probability because it is based on past observations of employee retention.

Question 18

An intuitive way to express the total probability rule is with the help of a _______________.

Accepted Answer

The answer of An intuitive way to express the total...

Question 19

What is probability?
A) Any value between 0 and 1 is always treated as a probability of an event.
B) A numerical value assigned to an event that measures the number of its occurrences.
C) A value between 0 and 1 assigned to an event that measures the likelihood of its occurrence.
D) A value between 0 and 1 assigned to an event that measures the unlikelihood of its occurrence.

Accepted Answer

Probability is defined as a value between 0 and 1 assigned to an event that measures the likelihood of its occurrence. Option A is partially correct but not comprehensive as probability is not just any value between 0 and 1, but specifically a measure of likelihood. Option B is incorrect as probability is not a count of occurrences. Option D is incorrect as probability measures the likelihood, not the unlikelihood, of an event happening.

Question 20

Which of the following is not an event when considering the sample space of tossing two coins?
A) {HH,HT}
B) {HH,TT,HT}
C) {HH,TT,HTH}
D) {HH,HT,TH,TT}

Accepted Answer

The third option {HH,TT,HTH} includes "HTH" which is not a possible outcome of tossing two coins. The only possible outcomes for two coin tosses are HH, HT, TH, and TT.

Quiz 4: Basic Probability Concepts

Events are collectively exhaustive if _____________.

In an experiment in which a coin is tossed twice,which of the following represents mutually exclusive and collectively exhaustive events?

Mutually exclusive and collectively exhaustive events ______________.

A sample space contains _________________.

For the sample space S = {apple pie,cherry pie,peach pie,pumpkin pie},what is the complement of A = {pumpkin pie,cherry pie}?

If A and B are _ __ events,then the addition rule is defined as

Events are considered _________ if the occurrence of one is related to the probability of the occurrence of the other.

What is a simple event?

Which of the following represents a subjective probability?

A probability based on logical analysis rather than on observation or personal judgment is best referred to as a(n) _______________.

An analyst has a limit order outstanding on a stock.He argues that the probability that the order will execute before the close of trading is 0.20.Thus,the odds for the order executing before the close of trading are

Which of the following are mutually exclusive events of an experiment in which two coins are tossed?

For an experiment in which a single die is rolled,the sample space is __________.

An analyst believes the probability that U.S.stock returns exceed long-term corporate bond returns over a five-year period is based on personal assessment.This type of probability is best characterized as a(n) ___________.

Assume the sample space S = {win,loss}.Select the choice that fulfills the requirements of the definition of probability.

Mutually exclusive events _____________.

Which of the following represents an empirical probability?

An intuitive way to express the total probability rule is with the help of a _______________.

What is probability?

Which of the following is not an event when considering the sample space of tossing two coins?