Question 1

Given an experiment in which a fair coin is tossed three times,the sample space is S = {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}.Event A is defined as tossing one head (H).What is the event A^C and what is the probability of this event?

Accepted Answer

Event A is defined as tossing exactly one head, which corresponds to {HTT, THT, TTH}. The complement A^C includes all outcomes except these, which are {TTT, HHT, HTH, THH, HHH}. The probability of A^C is the number of outcomes in A^C divided by the total number of outcomes, which is 5/8 = 0.625.

Question 2

The odds for encountering rain on a 500-mile car trip are 3 to 1.What is the probability of rain on this trip?

Accepted Answer

The answer of The odds for encountering rain on a...

Question 3

Let  ,and  .Calculate  .

Accepted Answer

The answer of Let  ,and  .Calculate  .
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Question 4

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

Accepted Answer

The probabilities given in option B add up to 1, as required for a probability distribution. Option A has a total probability greater than 1, which is impossible. Option C has a total probability greater than 1, which is impossible. Option D has a negative probability, which is impossible.

Question 5

Mutually exclusive and collectively exhaustive events ______________.

Accepted Answer

Mutually exclusive and collectively exhaustive events contain all outcomes in a sample space and do not share common outcomes. This means that if one event occurs, the others cannot occur simultaneously, and no outcomes are left unaccounted for.

Question 6

Which of the following represents a subjective probability?

Accepted Answer

A subjective probability is a probability that is determined subjectively, based on personal judgment, belief, or opinion. Choice C represents a subjective probability because it is based on the skier's personal belief about her chance of winning a gold medal. The other choices represent objective probabilities (based on statistical analysis or physical laws) or empirical probabilities (based on past observations or experiments).

Question 7

An analyst believes the probability that U.S.stock returns exceed long-term corporate bond returns over a 5-year period is based on personal assessment.This type of probability is best characterized as a(n)___________.

Accepted Answer

The probability based on personal assessment is subjective probability. It is determined subjectively by an individual's personal judgment or opinion.

Question 8

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 ________.

Accepted Answer

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

Question 9

Let  ,and  .Calculate  .

Accepted Answer

The answer of Let  ,and  .Calculate  .
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Question 10

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

Accepted Answer

Mutually exclusive events are events that cannot occur at the same time, while collectively exhaustive events are events that cover all possible outcomes. In option A, the events {TT,HH} and {TT,HT} are not mutually exclusive since {TT} is in both sets. Option B has events that are mutually exclusive, but not collectively exhaustive since it doesn't include {TT}. Option D has mutually exclusive events, but not collectively exhaustive since it doesn't include {HH}. Option C has mutually exclusive events {TT,HH} and {TH,HT}, and they are collectively exhaustive since they cover all the possible outcomes when a coin is tossed twice. Therefore, the best choice is C.

Question 11

An experiment consists of tossing three fair coins.What is the probability of tossing two tails?

Accepted Answer

There are 8 possible outcomes (HHH, HHT, HTH, THH, TTH, THT, HTT, TTT). Out of these 8, there are 3 outcomes where two tails are tossed (TTH, THT, HTT). Therefore, the probability of tossing two tails is 3/8.

Question 12

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

Accepted Answer

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

Question 13

The complement of an event A,within the sample space S,is the event consisting of ____________.

Accepted Answer

The complement of an event A within the sample space S consists of all outcomes in S that are not in A. Therefore, choice C is the correct answer. Choices A and D are incorrect because outcomes in A that are not in S cannot be part of the complement, and outcomes in A that are in S are already part of A. Choice B is also incorrect because outcomes in S that are in A are already part of A, and the complement consists of outcomes that are not in A.

Question 14

Which of the following represents an empirical probability?

Accepted Answer

Empirical probability is based on observed data or past experience. In option D, the probability is based on past observation, making it empirical.

Question 15

The union of events A and B,denoted by  ,____________.

Accepted Answer

The union of events A and B contains all the outcomes that are in A or B, meaning that if an outcome is in either A or B or both, it will be in the union of A and B.

Question 16

The intersection of events A and B,denoted by  ,___________.

Accepted Answer

The intersection of events A and B contains outcomes that are both in A and B. This is because the intersection of two sets is defined as the set of elements that are common to both sets. Therefore, any outcome that belongs to both A and B will be in the intersection of A and B.

Question 17

The intersection of events A = {apple pie,peach pie,pumpkin pie} and B = {cherry pie,blueberry pie,pumpkin pie} is ____________.

Accepted Answer

The intersection of two events consists of the elements that are in both events. Therefore, the only item that appears in both A and B is pumpkin pie.

Question 18

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

Accepted Answer

A priori probability is based on logical analysis, and not on personal judgment or observation. It is derived purely from mathematical reasoning or deduction, and is often used in situations where little data or empirical evidence is available.

Question 19

The odds against winning $1.00 in the lottery are 19 to 1.What is the probability of winning $1.00 in the lottery?

Accepted Answer

The answer of The odds against winning $1.00 in the...

Question 20

After extensive research,an analyst asserts that there is an 80% chance that ABC Corporation will beat its EPS forecast.Analogously,the odds for the company beating its EPS forecast are _______.

Accepted Answer

The odds are the ratio of the probability of an event occurring to the probability of it not occurring. In this case, the probability of ABC Corporation beating its EPS forecast is 0.8, and the probability of it not occurring is 0.2. Therefore, the odds are 0.8/0.2 = 4 to 1.

Quiz 4: Basic Probability Concepts

Given an experiment in which a fair coin is tossed three times,the sample space is S = {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}.Event A is defined as tossing one head (H) .What is the event A^C and what is the probability of this event?

The odds for encountering rain on a 500-mile car trip are 3 to 1.What is the probability of rain on this trip?

Let ,and .Calculate .

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

Mutually exclusive and collectively exhaustive events ______________.

Which of the following represents a subjective probability?

An analyst believes the probability that U.S.stock returns exceed long-term corporate bond returns over a 5-year period is based on personal assessment.This type of probability is best characterized 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 ________.

Let ,and .Calculate .

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

An experiment consists of tossing three fair coins.What is the probability of tossing two tails?

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

The complement of an event A,within the sample space S,is the event consisting of ____________.

Which of the following represents an empirical probability?

The union of events A and B,denoted by ,____________.

The intersection of events A and B,denoted by ,___________.

The intersection of events A = {apple pie,peach pie,pumpkin pie} and B = {cherry pie,blueberry pie,pumpkin pie} is ____________.

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

The odds against winning $1.00 in the lottery are 19 to 1.What is the probability of winning $1.00 in the lottery?

After extensive research,an analyst asserts that there is an 80% chance that ABC Corporation will beat its EPS forecast.Analogously,the odds for the company beating its EPS forecast are _______.

Quiz 4: Basic Probability Concepts

Given an experiment in which a fair coin is tossed three times,the sample space is S = {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}.Event A is defined as tossing one head (H) .What is the event AC and what is the probability of this event?

The odds for encountering rain on a 500-mile car trip are 3 to 1.What is the probability of rain on this trip?

Let ,and .Calculate .

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

Mutually exclusive and collectively exhaustive events ______________.

Which of the following represents a subjective probability?

An analyst believes the probability that U.S.stock returns exceed long-term corporate bond returns over a 5-year period is based on personal assessment.This type of probability is best characterized 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 ________.

Let ,and .Calculate .

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

An experiment consists of tossing three fair coins.What is the probability of tossing two tails?

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

The complement of an event A,within the sample space S,is the event consisting of ____________.

Which of the following represents an empirical probability?

The union of events A and B,denoted by ,____________.

The intersection of events A and B,denoted by ,___________.

The intersection of events A = {apple pie,peach pie,pumpkin pie} and B = {cherry pie,blueberry pie,pumpkin pie} is ____________.

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

The odds against winning $1.00 in the lottery are 19 to 1.What is the probability of winning $1.00 in the lottery?

After extensive research,an analyst asserts that there is an 80% chance that ABC Corporation will beat its EPS forecast.Analogously,the odds for the company beating its EPS forecast are _______.

Given an experiment in which a fair coin is tossed three times,the sample space is S = {HHH,HHT,HTH,THH,HTT,THT,TTH,TTT}.Event A is defined as tossing one head (H) .What is the event A^C and what is the probability of this event?