Deck 4: Basic Probability Concepts

Question 1

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

Answer 1

{2,1,3,6,5,4}

Question 2

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

Answer 2

True

Question 3

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

Answer 3

True

Question 4

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 5

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 6

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

Question 7

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 8

Mutually exclusive and collectively exhaustive events contain all outcomes of a sample space,and they do not share any common outcomes.

Question 9

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 10

The intersection of two events A and B,denoted by A ∩ B,is the event consisting of all outcomes that are in A and B

Question 11

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 12

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 13

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 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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

Question 20

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

Question 21

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 22

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

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

Question 23

Let ,and .Calculate .

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

Question 24

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 25

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 26

Which of the following represents a subjective probability?

A)The probability of rolling a 2 on a single die is 1 in 6.
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 3-in-5 chance of retaining an employee for at least one year.

Question 27

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)___________.

A)A priori probability
B)Empirical probability
C)Objective probability
D)Subjective probability

Question 28

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)1 in 4
B)1 in 5
C)4 to 1
D)5 to 1

Question 29

Let ,and .Calculate .

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

Question 30

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 31

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 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

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

A)All outcomes in A that are in S
B)All outcomes in S that are in A
C)All outcomes in S that are not in A
D)All outcomes in A that are not in S

Question 34

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 1 in 6.
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 3-in-5 chance of retaining an employee for at least one year.

Question 35

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

A)Contains all outcomes that are in A or B
B)Contains all outcomes of an experiment
C)Contains no outcomes that are in A and B
D)Consists only of outcomes that are in A and B

Question 36

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

A)Contains outcomes that are either in A or B
B)Contains outcomes that are both in A and B
C)Does not contain outcomes that are either in A or B
D)Does not contain outcomes that are both in A and B

Question 37

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

A){pumpkin pie}
B){apple pie,peach pie,cherry pie,blueberry pie}
C){apple pie,peach pie,pumpkin pie,cherry pie,blueberry pie}
D){apple pie,peach pie,pumpkin pie,cherry pie,blueberry pie,pumpkin pie}

Question 38

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 39

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 40

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)1 in 4
B)1 in 1.25
C)4 to 1
D)1.25 to 1

Question 41

Exhibit 4-3.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. Refer to Exhibit 4-3.What is the probability that a randomly selected customer prefers vanilla?

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

Question 42

Exhibit 4-3.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. Refer to Exhibit 4-3.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 43

Exhibit 4-1.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. Refer to Exhibit 4-1.The probability that a respondent read a book in the last month and is at least 30 years old is closest to _______.

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

Question 44

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35 and those 35 years of age or older.Find the probability that an individual prefers running.

A)0.3159
B)0.3915
C)0.6085
D)0.6805

Question 45

Exhibit 4-2.Mark Zuckerberg,the founder of Facebook,has 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. Refer to Exhibit 4-2.The probability that a respondent to the survey is male is closest to ____.

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

Question 46

The following probability table shows probabilities concerning Favorite Subject and Gender.What is the probability of selecting an individual preferring science given that he/she is a female?

A)0.2609
B)0.4615
C)0.5385
D)0.7391

Question 47

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 48

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 49

The following probability table shows probabilities concerning Favorite Subject and Gender.What is the probability of selecting an individual who is a female or prefers science?

A)0.250
B)0.375
C)0.625
D)0.750

Question 50

Exhibit 4-3.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. Refer to Exhibit 4-3.What is the probability a randomly selected customer prefers chocolate swirled yogurt or is at least 25 years old?

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

Question 51

The contingency table below provides frequencies for the preferred type of exercise for people under the age of 35,and those 35 years of age or older.Find the probability that an individual prefers biking given that he/she is 35 years old or older.

A)0.1698
B)0.1824
C)0.8175
D)0.8302

Question 52

Exhibit 4-1.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. Refer to Exhibit 4-1.The probability that a respondent is at least 30 years old is closest to ______.

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

Question 53

Find the missing values marked xx and yy in the following contingency table:

A)xx = 72,yy = 79
B)xx = 27,yy = 77
C)xx = 27,yy = 79
D)xx = 72,yy = 77

Question 54

Exhibit 4-2.Mark Zuckerberg,the founder of Facebook,has 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. Refer to Exhibit 4-2.Given that the respondent is male,the probability that he feels that the idea of killing his own food is appealing is closest to ____.

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

Question 55

Exhibit 4-2.Mark Zuckerberg,the founder of Facebook,has 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. Refer to Exhibit 4-2.The probability that a respondent is male and feels that the idea of killing his own food is appealing is closest to _____.

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

Question 56

Let A and B be two independent events with P(A)= 0.40 and P(B)= 0.20.Therefore,__________.

A)
B)
C)
D)

Question 57

If A and B are independent events,then _________.

A)
B)
C)
D)

Question 58

Exhibit 4-1.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. Refer to Exhibit 4-1.Given that a respondent read a book in the last month,the probability that he/she is at least 30 years old is closest to ________.

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

Question 59

Let and .Suppose A and B are independent.What is ?

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

Question 60

The likelihood of Company A's stock price rising is 20 percent,and the likelihood of Company B's stock price rising is 30 percent.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 61

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 62

Let , ,and .Compute .

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

Question 63

An experiment consists of tossing a fair coin and rolling a fair die.Find the probability that we toss a head and roll a 6.

Question 64

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 65

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 4 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 66

How many ways can a potential 4-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 67

Let ,and .Compute .

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

Question 68

Let ,and .Compute .

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

Question 69

Let ,and .Compute .

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

Question 70

An experiment consists of rolling a fair die.Find the probability that we roll a 4 or a 6.

Question 71

An analyst expects that 20 percent 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' theorem,the posterior probability that the company will experience a decline is ____.

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

Question 72

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 73

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 74

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

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

Question 75

An analyst expects that 10 percent 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' theorem,the posterior probability that the company will experience a decline is ____.

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

Question 76

How many project teams composed of 5 students can be created out of a class of 10 students?

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

Question 77

The following table summarizes the ages of the 400 richest Americans.Suppose we select one of these individuals.Find the probability that the selected individual is at least 60 years old.

Question 78

The following table summarizes the ages of the 400 richest Americans.Suppose we select one of these individuals.Find the probability that the selected individual is less than 80 years old.

Question 79

Let ,and .Compute .

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

Question 80

The likelihood of rain has been reported at 80% for next week.Find the odds for rain occurring.