Deck 4: Basic Probability Concepts

Question 1

Events are exhaustive if they do not share common outcomes of a sample space.

Answer 1

False

Question 2

Bayes's theorem is a rule that uses the total probability rule and the addition rule to update the probability of the event.

Answer 2

False

Question 3

Consider the following events:
A = The survey respondent is less than 40 years old.
B = The survey respondent is 40 years or older.
Events A and B are mutually exclusive and exhaustive.

Answer 3

True

Question 4

Permutations are used when the order in which different objects are arranged matters.

Question 5

Probabilities can be expressed as fractions,percentages,and ______.

Question 6

Combinations are used when the order in which different objects are arranged matters.

Question 7

Counting rules are important when calculating a(n)________ probability.

Question 8

For two independent events A and B,the probability of their intersection is zero.

Question 9

For an experiment in which a single die is rolled,the sample space may be {1,1,2,3,4,5}.

Question 10

The complement of an event A,denoted by A^C,within the sample space S,is the event consisting of all outcomes of A that are not in S.

Question 11

Subjective probability is assigned to an event by drawing on logical analysis.

Question 12

The total probability rule is useful only when the unconditional probability is expressed in terms of probabilities conditional on two mutually exclusive and exhaustive events.

Question 13

Bayes's theorem is used to update prior probabilities based on the arrival of new relevant information.

Question 14

Mutually exclusive events may share common outcomes of a sample space.

Question 15

A(n)________ probability is calculated as the relative frequency with which an event occurs.

Question 16

The probability of a union of events can be greater than 1.

Question 17

The addition rule is used to determine the probability of the union of two events occurring and is defined as a sum of the probabilities of both events.

Question 18

Bayes's theorem uses the total probability rule to update the prior probability of an event that has not been affected by any new evidence.

Question 19

A(n)_____ _____ of an experiment records all possible outcomes of the experiment.

Question 20

The total probability rule is defined as P(A)= P(A B)P(A )

Question 21

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.

Question 22

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}

Question 23

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.

Question 24

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.

Question 25

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}

Question 26

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

Question 27

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

Question 28

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

Question 29

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.

Question 30

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.

Question 31

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.

Question 32

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}

Question 33

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

Question 34

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.

Question 35

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

Question 36

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.

Question 37

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.

Question 38

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

Question 39

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.

Question 40

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}

Question 41

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

A) 0.05
B) 0.0526
C) 0.90
D) 0.95

Question 42

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

A) 0.25
B) 0.33
C) 0.50
D) 0.75

Question 43

Mark Zuckerberg,the founder of Facebook,announced that he will eat meat only from animals that he has killed himself (Vanity Fair,November 2011).Suppose 257 people were asked,"Does the idea of killing your own food appeal to you,or not?" The accompanying contingency table,cross-classified by gender,is produced from the 187 respondents. Given that the respondent is male,the probability that he feels that the idea of killing his own food is appealing is the closest to ____.

A) 0.19.
B) 0.38.
C) 0.59.
D) 0.64.

Question 44

Let Suppose A and B are independent.What is the value of P(B|A)?

A) 0.12
B) 0.3
C) 0.4
D) 0.7

Question 45

If A and B are independent events,which of the following is correct?

A)
B)
C)
D)

Question 46

Two hundred people were asked if they had read a book in the last month.The accompanying contingency table,cross-classified by age,is produced. Given that a respondent read a book in the last month,the probability that he or she is at least 30 years old is the closest to ________.

A) 0.33.
B) 0.46.
C) 0.65.
D) 0.88.

Question 47

Let A and B be two independent events with P(A)= 0.40 and P(B)= 0.20.Which of the following is correct?

A)
B)
C)
D)

Question 48

The likelihood of Company A's stock price rising is 20%,and the likelihood of Company B's stock price rising is 30%.Assume that the returns of Company A and Company B stock are independent of each other.The probability that the stock price of at least one of the companies will rise is ______.

A) 6%.
B) 10%.
C) 44%.
D) 50%.

Question 49

Peter applied to an accounting firm and a consulting firm.He knows that 30% of similarly qualified applicants receive job offers from the accounting firm,while only 20% of similarly qualified applicants receive job offers from the consulting firm.Assume that receiving an offer from one firm is independent of receiving an offer from the other.What is the probability that both firms offer Peter a job?

A) 0.05
B) 0.06
C) 0.44
D) 0.50

Question 50

Two hundred people were asked if they had read a book in the last month.The accompanying contingency table,cross-classified by age,is produced. The probability that a respondent is at least 30 years old is the closest to ______.

A) 0.33.
B) 0.46.
C) 0.50.
D) 0.65.

Question 51

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

A) 1/8
B) 1/4
C) 3/8
D) 1/2

Question 52

Mark Zuckerberg,the founder of Facebook,announced that he will eat meat only from animals that he has killed himself (Vanity Fair,November 2011).Suppose 257 people were asked,"Does the idea of killing your own food appeal to you,or not?" The accompanying contingency table,cross-classified by gender,is produced from the 187 respondents. The probability that a respondent is male and feels that the idea of killing his own food is appealing is the closest to _____.

A) 0.19.
B) 0.38.
C) 0.41.
D) 0.59.

Question 53

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 _______.

A) one in four
B) 1 in 1.25
C) four to one
D) 1.25 to 1

Question 54

Two hundred people were asked if they had read a book in the last month.The accompanying contingency table,cross-classified by age,is produced. The probability that a respondent read a book in the last month and is at least 30 years old is the closest to _______.

A) 0.12.
B) 0.33.
C) 0.46.
D) 0.88.

Question 55

Mark Zuckerberg,the founder of Facebook,announced that he will eat meat only from animals that he has killed himself (Vanity Fair,November 2011).Suppose 257 people were asked,"Does the idea of killing your own food appeal to you,or not?" The accompanying contingency table,cross-classified by gender,is produced from the 187 respondents. The probability that a respondent to the survey is male is the closest to ____.

A) 0.19.
B) 0.38.
C) 0.49.
D) 0.64.

Question 56

Let .Calculate .

A) 0.20
B) 0.33
C) 0.40
D) Not enough information to calculate.

Question 57

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?

A) A^c = {TTT,HHH,HTH};P(A^c)= 0.375
B) A^c = {TTT,THH,HHH,HHT};P(A^c)= 0.500
C) A^c = {TTT,HHH,HHT,HTH,HTT};P(A^c)= 0.625
D) A^c = {TTT,HHT,HTH,THH,HHH};P(A^c)= 0.625

Question 58

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla,chocolate,or swirled frozen yogurt.The results are displayed next. What is the probability that a randomly selected customer prefers vanilla?

A) 0.13
B) 0.27
C) 0.33
D) 0.40

Question 59

A recent survey shows that the probability of a college student drinking alcohol is 0.6.Further,given that the student is over 21 years old,the probability of drinking alcohol is 0.8.It is also known that 30% of the college students are over 21 years old.The probability of drinking or being over 21 years old is __________.

A) 0.24.
B) 0.42.
C) 0.66.
D) 0.90.

Question 60

Let P(A)= 0.6,P(B)= 0.5,and .Calculate .

A) 0.2
B) 0.3
C) 0.9
D) Not enough information to calculate.

Question 61

An analyst expects that 20% of all publicly traded companies will experience a decline in earnings next year.The analyst has developed a ratio to help forecast this decline.If the company is headed for a decline,there is a 90% chance that this ratio will be negative.If the company is not headed for a decline,there is only a 10% chance that the ratio will be negative.The analyst randomly selects a company with a negative ratio.Based on Bayes's theorem,the posterior probability that the company will experience a decline is

A) 18%.
B) 26%.
C) 44%.
D) 69%.

Question 62

Let P(A)= 0.4,P(B|A)= 0.5,and P(B|A^c)= 0.25.Compute P(A|B).

A) 0.20
B) 0.35
C) 0.57
D) 0.80

Question 63

A survey of adults who typically work full time from home recorded their current education level.The results are shown in the table below. Calculating the probability that a randomly selected adult who works full time from home has an associate degree is using ________ probability.

A) empirical
B) simple
C) subjective
D) classical

Question 64

A small company that manufactures juggling equipment makes seven different types of clubs.The company wants to start an ad campaign that emphasizes the myriad combinations the avid juggler can create with the company's clubs.If a juggler wishes to juggle four clubs,each of a different type,how many different combinations of the company's clubs can he or she make?

A) 7
B) 28
C) 35
D) 210

Question 65

A random sample of computer users was asked which browser they primarily relied on for surfing the Internet and whether this browser was installed on a PC or on a Mac computer.The following contingency table shows these results.

A) 0.235
B) 0.320
C) 0.361
D) 0.443

Question 66

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla,chocolate,or swirled frozen yogurt.The results are displayed next. What is the probability a randomly selected customer prefers swirled yogurt or is at least 25 years old?

A) 0.10
B) 0.20
C) 0.77
D) 0.90

Question 67

How many ways can a committee of four students be selected from a 15-member club?

A) 15!/44!
B) 15!/(11! ×4!)
C) 15 ×14 ×13
D) B and C

Question 68

A survey of adults who typically work full time from home recorded their current education level.The results are shown in the table below. The probability that a randomly selected adult who works full time from home has a bachelor's degree or higher is ______.

A) 0.24.
B) 0.29.
C) 0.33.
D) 0.64.

Question 69

When some objects are randomly selected,which of the following is true?

A) The order in which objects are selected matters in combinations.
B) The order in which objects are selected does not matter in permutations.
C) The order in which objects are selected does not matter in combinations.
D) The order in which objects are selected matters in both permutations and combinations.

Question 70

Let ,and .Compute .

A) 0.33
B) 0.45
C) 0.5
D) 0.67

Question 71

Let P(A)= 0.4,P(B|A)= 0.5,and P(B|A^c)= 0.25.Compute P(B).

A) 0.125
B) 0.15
C) 0.20
D) 0.35

Question 72

Romi,a production manager,is trying to improve the efficiency of his assembly line.He knows that the machine is set up correctly only 60% of the time.He also knows that if the machine is set up correctly,it will produce good parts 80% of the time,but if set up incorrectly,it will produce good parts only 20% of the time.Romi starts the machine and produces one part before he begins the production run.He finds the first part to be good.What is the revised probability that the machine was set up correctly?

A) 48%
B) 56%
C) 86%
D) 96%

Question 73

How many ways can a potential four-letter word,whether or not it has a meaning,be created out of 10 available different letters?

A) 4 * 3 * 2 * 1
B) 10 * 9 * 8 * 7/(4 * 3 * 2)
C) 10 * 9 * 8 * 7 * 6 * 5/(4 * 3 * 2)
D) 10 * 9 * 8 * 7

Question 74

How many project teams composed of five students can be created out of a class of 10 students?

A) 10
B) 50
C) 252
D) 30,240

Question 75

Let ,and ,and .Compute .

A) 0.20
B) 0.50
C) 0.65
D) 0.70

Question 76

Romi,a production manager,is trying to improve the efficiency of his assembly line.He knows that the machine is set up correctly only 70% of the time.He also knows that if the machine is set up correctly,it will produce good parts 95% of the time,but if set up incorrectly,it will produce good parts only 40% of the time.Romi starts the machine and produces one part before he begins the production run.He finds the first part to be good.What is the revised probability that the machine was set up correctly?

A) 12%
B) 33.5%
C) 66.5%
D) 84.7%

Question 77

Let ,and .Compute P(A).

A) 0.15
B) 0.30
C) 0.45
D) 0.50

Question 78

The 150 residents of the town of Wonderland were asked their age and whether they preferred vanilla,chocolate,or swirled frozen yogurt.The results are displayed next. What is the probability a randomly selected customer prefers chocolate given he or she is at least 25 years old?

A) 0.10
B) 0.20
C) 0.27
D) 0.77

Question 79

Boeing currently produces five models of airplanes for commercial sale.The airline that Lauren works for is rapidly expanding and would like to purchase three airplanes of different models to service various routes.Her job is to analyze which three to buy.How many combinations will she have to analyze?

A) 5
B) 10
C) 15
D) 20

Question 80

An analyst expects that 10% of all publicly traded companies will experience a decline in earnings next year.The analyst has developed a ratio to help forecast this decline.If the company is headed for a decline,there is a 70% chance that this ratio will be negative.If the company is not headed for a decline,there is only a 20% chance that the ratio will be negative.The analyst randomly selects a company and its ratio is negative.Based on Bayes's theorem,the posterior probability that the company will experience a decline is ____.

A) 3%.
B) 7%.
C) 18%.
D) 28%.