Deck 4: Probability

Question 1

If events A and B are independent, then P(A) = P(A|B).

Answer 1

True

Question 2

Two events A and B are said to be mutually exclusive if the occurrence of one event means that the other event cannot or will not occur; that is P(A $\cap$ B) = 0.

Answer 2

True

Question 3

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the subjective method.

Answer 3

False

Question 4

In a multi-stage experiment, if there are two outcomes per stage and there are three stages, then the total number of outcomes is six.

Question 5

Drew is a long-time employee at your coffee shop.Which would be the most appropriate method for estimating the probability that Drew will be on time to work next Monday morning?

A)the classical approach
B)the relative frequency approach
C)the subjective approach
D)the experimental method
E)none of the above

Question 6

In constructing a probability tree, probabilities beyond the first stage are conditional probabilities and the multiplication rule is used to get end node probabilities.

Question 7

When the results of experimentation or historical data are used to assign probability values, the method used to assign probabilities is referred to as the:

A)relative frequency method
B)subjective method
C)classical method
D)posterior method
E)none of the above

Question 8

Probability is a number between 0 and 1 that measures the chance or likelihood that some event or set of events will occur.

Question 9

For the cases listed below, in which one would you most likely use the classical approach to assign probability?

A)the probability that at least one of the ten orders you placed on Amazon will be delivered late.
B)the probability that you will become famous.
C)the probability that you roll a five on one roll of two dice.
D)the probability that you it will snow be cloudy tomorrow.
E)the probability that you will pass the exam today.

Question 10

A probability near 1 for an event indicates that the event is very unlikely to occur.

Question 11

A graphical method of representing the sample points or outcomes of a multiple step experiment is a Venn diagram.

Question 12

Which of the following is NOT one of the basic requirements of probability?

A)for each experimental outcome E_i, then 0 < P(E_i) < 1 for all i
B)P(A) = P(A^') - 1
C)if there are k experimental outcomes, then P(E₁) + P(E₂) + … + P(E_k) = 1
D)both b and c
E)all of the above

Question 13

If events A and B are mutually exclusive, then P(A or B) = P(A)+P(B).

Question 14

One of the basic requirements of probability is:

A)for each experimental outcome E_i, we must have P(E_i) $\ge$ 1
B)P(A) = P(A^') - 1
C)if there are k experimental outcomes, then P(E₁) + P(E₂) + … + P(E_k) = 1
D)both b and c
E)all of the above

Question 15

Two events are mutually exclusive if the probability of their intersection is 0.5.

Question 16

For the cases listed below, in which one would you most likely use the subjective approach to assign probability?

A)the probability of being chosen randomly from your class of 30 students to lead today's class discussion.
B)the probability that your friend Kyle will pick up the check for lunch.
C)the probability that you will guess the right answer on a multiple choice test question.
D)the probability that you produce at least ten heads when you flip a quarter 20 times.
E)the probability that you will an ace of spades from a 52-card deck of cards.

Question 17

A probability near 0 for an event indicates that the event is very likely to occur.

Question 18

Each individual outcome of an experiment is called a sample point.

Question 19

Probability is defined as the numerical measure of the likelihood that an event will occur and is always between 0 and 1.

Question 20

If events A and B are independent, then P(A and b) = P(A)*P(B).

Question 21

A useful counting method that enables us to count the number of experimental outcomes when x objects are to be selected from a set of n objects, where the order of selection is NOT important is:

A)a combination
B)a permutation
C)the multiplication method
D)joint probability table
E)none of the above

Question 22

When the results of experimentation or historical data are used to assign probability values, the is used to assign probabilities.

A)relative frequency method
B)subjective method
C)classical method
D)posterior method
E)none of the above

Question 23

Which of the following illustrates the concept of statistically independent?

A)P(A|B) = P(A)
B)P(A $\cap$ B) = P(A)*P(B)
C)P(A $\cup$ B) = P(A) + P(B)
D)a and b only
E)all of the above

Question 24

In a Venn diagram, if the circles representing the probability of A and the probability of B overlap,

A)A and B are not statistically independent.
B)A and B are not mutually exclusive.
C)the multiplication rule can be used to find the joint probability.
D)both a and b are true.
E)none of the above.

Question 25

The addition law is potentially helpful when we are interested in computing the probability of:

A)independent events.
B)the intersection of two events.
C)the union of two events.
D)conditional events.
E)complimentary events.

Question 26

An experiment consists of four outcomes with P(E₁) = 0.2, P(E₂) = 0.25, and P(E₃) = 0.35.The probability of P(E₄) is:

A)0.50
B)0.90
C)0.20
D)0.10
E)none of the above

Question 27

The union of events A and B is the event containing:

A)all the sample points common to both A and B
B)all the sample points belonging to A or B
C)all the sample points belonging to A or B or both
D)all the sample points belonging to A or B, but not both
E)none of the above

Question 28

If two events are independent, then:

A)they must be mutually exclusive
B)the sum of their probabilities must be equal to one
C)the probability of their intersection must be zero
D)all of the above
E)none of the above

Question 29

A useful counting method that enables us to count the number of experimental outcomes when x objects are to be selected from a set of n objects, where the order of selection does matter is:

A)a combination
B)a permutation
C)the multiplication method
D)joint probability table
E)none of the above

Question 30

The joint probability of A and B is determined by:

A)adding the probabilities of A and B.
B)multiplying the probability of A by the probability of B.
C)multiplying the probability of A by the conditional probability of A given B.
D)multiplying the probability of A by the conditional probability of B given A.
E)dividing the conditional probability of B given A by the probability of B

Question 31

A perfectly balanced coin is tossed 6 times and tails appears on all six tosses.Then, on the seventh trial:

A)tails cannot appear
B)heads has a larger chance of appearing than tails
C)tails has a better chance of appearing than heads
D)heads and tails both have an equal chance of appearing
E)none of the above

Question 32

The conditional probability of A given B:

A)will always be less than the simple probability of A.
B)will always be greater than the simple probability of A.
C)will always be equal to or less than the simple probability of A.
D)will always be 0 if A and B are mutually exclusive.
E)will always be equal to the simple probability of B.

Question 33

An experiment consists of four outcomes with P(E₁) = 0.2, P(E₂) = 0.3, and P(E₃) = 0.4.The probability of P(E₄) is:

A)0.50
B)0.90
C)0.02
D)0.10
E)none of the above

Question 34

The probability of the intersection of two mutually exclusive events:

A)can be any value between 0 and 1.
B)must always be equal to 1.
C)must always be equal to 0.
D)can be any positive value.
E)none of the above.

Question 35

If two events A and B are complementary,

A)they must also be mutually exclusive.
B)they must also be statistically independent.
C)the probabilities of the two events must sum to one.
D)both a and b are true.
E)none of the above.

Question 36

The is potentially helpful when we are interested in computing the probability of the union of two events.

A)multiplication rule
B)the complimentary rule
C)addition rule
D)joint probability rule
E)the joint over simple rule

Question 37

If two events A and B are statistically independent, then:

A)A's occurrence makes it less likely that B will occur.
B)A's occurrence makes it more likely that B will occur.
C)A's occurrence makes it impossible that B will occur.
D)A's occurrence has no effect on the probability of B occurring.
E)B's occurrence has minimal effect on the probability of A occurring.

Question 38

Which of the following pairs of events would seem to be mutually exclusive?

A)Vacationing next week in Hawaii and vacationing next week in Paris.
B)Ordering a hamburger for dinner and ordering French fries for dinner.
C)Enrolling in a math class and enrolling in a Spanish class next quarter.
D)Majoring in economics and playing on the soccer team.
E)Eating a sandwich for lunch and drinking a glass of milk for lunch.

Question 39

Which of the following event pair would seem to be mutually exclusive?

A)A = studying 12 hours a day.B = sleeping 15 hours a day.
B)A = swimming a mile each day.B = having a full-time job.
C)A = playing professional basketball.B = making a million dollars.
D)A = playing Angry Birds.B = playing Minecraft.
E)A = exercising regularly.B = listening to classical music.

Question 40

Which of the following statements is TRUE concerning a probability tree?

A)it is especially helpful when the experiment involves multiple steps/stages.
B)branches extend from each node.
C)each branch represents a possible outcome.
D)beyond the first step/stage, the branch probabilities are conditional probabilities.
E)all of the above.

Question 41

The table below shows six companies that were established within the last two years, along with each company's classification and current financial status (profitable or unprofitable).If one company will be randomly selected for closer study, what is the joint probability that the company selected is a Hi Tech company and is currently profitable?

A)1.0
B).333
C).167
D).667
E).00

Question 42

Below is a table showing the five department heads in Carlton-Manning's San Jose (CA) and Utica (NY) regional offices, along with each department head's forecast of sales in the upcoming quarter.One person from the group will be randomly chosen to make a sales presentation.Determine the simple probability of randomly selecting a person who forecasts a decrease in sales.

A).4
B).6
C).125
D).25
E).3

Question 43

Tobrix Corporation plans to introduce two new games this year.Analysts estimate a 60% probability that Teletron will be successful and a 50% probability that Monstroids will be successful.They agree that there is a 30% probability that both will be successful.How likely is it that either Teletron or Monstroids (or both) will be successful?

A).2
B).8
C).3
D).7 e .5

Question 44

The table below shows six companies that were established within the last two years, along with each company's classification and current financial status (profitable or unprofitable).One company from the group will be randomly chosen for closer study.Are the events "choosing a Lo Tech company" and "choosing an unprofitable company" statistically independent?

A)Yes, since P(Lo Tech given unprofitable) is equal to P(unprofitable).
B)Yes, since P(unprofitable given Lo Tech) is equal to P(Lo Tech).
C)Yes, since P(Lo Tech given unprofitable) is equal to P(Lo Tech).
D)No, since P(unprofitable given Lo Tech) is not equal to P(Lo Tech).
E)No, since P(profitable given Lo Tech) is not equal to P(Lo Tech).

Question 45

Below is a table showing the five department heads in Carlton-Manning's San Jose and Utica (N.Y.) regional offices, along with each department head's forecast of sales in the upcoming quarter.One person from the group will be randomly chosen to make a sales presentation.Determine the conditional probability that the person selected is from the San Jose office, given that the person forecasts a decrease in sales.

A).5
B).333
C).667
D).4
E).125

Question 46

The table below shows six companies that were established within the last two years, along with each company's classification and current financial status (profitable or unprofitable).If one company will be randomly selected for closer study, what is the conditional probability that the company selected is a Hi Tech company, given that the company is profitable?

A).333
B).5
C).25
D).667
E).4

Question 47

The table below shows six companies that were established within the last two years, along with each company's classification and current financial status (profitable or unprofitable).If one company will be randomly selected for closer study, what is the conditional probability that the company selected is unprofitable, given that the company is classified as low tech.

A).333
B).667
C).5
D).125
E).25

Question 48

A is a visual method that is especially helpful when the probability experiment involves multiple steps/stages.

A)probability tree
B)Venn diagram
C)scatter diagram
D)histogram
E)bar chart

Question 49

The method enables us to count the number of experimental outcomes when x objects are to be selected from a set of n objects, where the order of selection is important.

A)combination
B)permutation
C)multiplication method
D)joint probability table
E)probability tree

Question 50

Josh has been given two assignments, assignment A and assignment B.He estimates that the chance of getting a passing grade on assignment A is 60% and the chance of getting a passing grade on assignment B is 50%.If Josh gets a passing grade on assignment A, he figures his chances of getting a passing grade on assignment B increase to 70%.How likely is it that Josh gets a passing grade on assignment A but not on assignment B?

A).30
B).42
C).18
D).49
E).85

Question 51

Josh has been given two assignments, assignment A and assignment B.He estimates that the chance of getting a passing grade on assignment A is 60% and the chance of getting a passing grade on assignment B is 50%.If Josh gets a passing grade on assignment A, he figures his chances of getting a passing grade on assignment B increase to 70%.How likely is it that Josh gets a passing grade on assignment B but NOT on assignment A?

A).08
B).32
C).20
D).18
E).15

Question 52

Marcus works as a waiter on the weekends and in the evenings after classes.7% of the time he gets a customer's food order wrong.3% of the time he gets a customer's drink order wrong.2% of the time, he gets both orders wrong.According to these numbers, if Marcus gets the food order wrong for a customer, how likely is it that he gets the drink order wrong, as well?

A).210
B).286
C).140
D).060
E).568

Question 53

Josh has been given two assignments, assignment A and assignment B.He estimates that the chance of getting a passing grade on assignment A is 60% and the chance of getting a passing grade on assignment B is 50%.Assuming that assignment grades are statistically independent, how likely is it that Josh gets a passing grade on both assignments?

A)20%
B)50%
C)30%
D)10%
E)70%

Question 54

A can be used to show elements of basic probability and provide an effective visual basis for solving a wide range of probability problems.

A)probability tree
B)Venn diagram
C)scatter diagram
D)histogram
E)bar chart

Question 55

Josh has been given two assignments, assignment A and assignment B.He estimates that the chance of getting a passing grade on assignment A is 60% and the chance of getting a passing grade on assignment B is 50%.If Josh gets a passing grade on assignment A, he figures his chances of getting a passing grade on assignment B increase to 70%.How likely is it that Josh does NOT get a passing grade on either assignment?

A).85
B).32
C).20
D).18
E).15

Question 56

Eryn has just bought two stocks: A and B.She estimates that stock A has an 80% chance of increasing in value.She estimates that stock B has a 70% chance of increasing in value.She also estimates that if stock A increases in value, the chance that stock B will increase jumps to 75%.What's the probability that at least one of the stocks will increase in value?

A).24
B).20
C).26
D).90
E).56

Question 57

Eryn has just bought two stocks: A and B.She estimates that stock A has an 80% chance of increasing in value.She estimates that stock B has a 70% chance of increasing in value.She also estimates that if stock A increases in value, the chance that stock B will increase jumps to 75%.What's the probability that both stocks increase in value?

A).60
B).56
C).665
D).74
E).65

Question 58

Below is a table showing the five department heads in Carlton-Manning's San Jose (CA) and Utica (NY) regional offices, along with each department head's forecast of sales in the upcoming quarter.One person from the group will be randomly chosen to make a sales presentation.Determine the conditional probability that the person selected is from the San Jose office, given that the person forecasts an increase in sales.

A)1.0
B).333
C).5
D).667
E).00

Question 59

Below is a table showing the five department heads in Carlton-Manning's San Jose and Utica (N.Y.) regional offices, along with each department head's forecast of sales in the upcoming quarter.One person from the group will be randomly chosen to make a sales presentation.Are the events "choosing someone from the Utica office" and "choosing someone who forecasts a decrease in sales" statistically independent.

A)Yes, since P(San Jose given increase) is equal to P(increase).
B)Yes, since P(San Jose given increase) is equal to P(San Jose).
C)No, since P(San Jose given increase) is not equal to P(San Jose).
D)No, since P(San Jose given increase) is not equal to P(increase).
E)No, since P(San Jose given decrease) is not equal to P(decrease)

Question 60

Below is a table showing the five department heads in Carlton-Manning's San Jose and Utica (N.Y.) regional offices, along with each department head's forecast of sales in the upcoming quarter.One person from the group will be randomly chosen to make a sales presentation.Determine the simple probability of selecting a person from the Utica Office.

A).2
B).5
C).25
D).125
E)..4

Question 61

Your investment club plans to buy three stocks this semester and has narrowed the choice of stocks to a final ten- six US companies and four EU companies.From the ten finalists, you now plan to randomly select the three stocks to buy.What is the probability that you end up buying no US stocks?

A).064
B).127
C).056
D).129
E).033

Question 62

According to studies, 62% percent of online teenagers are Facebook users, while 51% are use Twitter.43% are both Facebook and Twitter users.Are the two events-uses Facebook and uses Twitter-statistically independent?

A)Yes, since P(Facebook given Twitter) is equal to P(Facebook).
B)Yes, since P(Facebook given Twitter) is equal to P(Twitter).
C)No, since P(Facebook given Twitter) is not equal to P(Twitter).
D)No, since P(Facebook given Twitter) is not equal to P(Facebook).
E)No, since P(Twitter given Facebook) is not equal to P(Facebook).

Question 63

Marcus works as a waiter on the weekends and in the evenings after classes.7% of the time he gets a customer's food order wrong.3% of the time he gets a customer's drink order wrong.Two percent of the time, he gets both orders wrong.According to these numbers, if Marcus gets a customer's drink order wrong, how likely is it that he gets the customer's food order wrong, as well?

A).333
B).060
C).667
D).210
E).014

Question 64

Marcus works as a waiter on the weekends and in the evenings after classes.7% of the time he gets a customer's food order wrong.3% of the time he gets a customer's drink order wrong.Two percent of the time, he gets both orders wrong.According to these numbers, are the two events-getting the drink order wrong and getting the food order wrong- statistically independent?

A)Yes, since P(wrong food given wrong drink) is equal to P(wrong food).
B)No, since P(wrong food given wrong drink) is not equal to P(wrong drink).
C)No, since P(wrong food given wrong drink) is not equal to P(wrong food).
D)Yes, P(wrong food given wrong drink) is equal to P(wrong drink).
E)Yes, P(wrong food given wrong drink) is equal to P(wrong food).

Question 65

The price of Chrysler stock increased on 30% of the trading days over the past year.The price of Ford stock increased on 40% of the trading days over the past year.On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well.On what proportion of the days did both stocks increase in price?

A).18
B).12
C).36
D).24
E).70

Question 66

The price of Chrysler stock increased on 30% of the trading days over the past year.The price of Ford stock increased on 40% of the trading days over the past year.On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well.On what proportion of the days did at least one stock increase in price?

A).54
B).46
C).12
D).88
E).22

Question 67

Antonia and Bethany played in the same 50 tennis matches last year.Antonia made the finals in 20 of those matches.Bethany made the finals in 15 of the matches.In 12 of the matches, they both made it to the finals.In what proportion of the matches where Antonia made the final did Bethany also make the final?

A).54
B).06
C).12
D).88
E).60

Question 68

If the probability that both Microsoft and Intel will have a significant growth in profits next year is 0.4, what is the probability that at least one of them will not?

A).4
B).6
C).667
D).333
E).5

Question 69

Antonia and Bethany played in the same 50 tennis matches last year.Antonia made the finals in 20 of those matches.Bethany made the finals in 15 of the matches.In 12 of the matches, they both made it to the finals.Are the events "Antonia makes it to the finals" and "Bethany makes it to the finals" statistically independent?

A)No, since P(Antonia given Bethany) is not equal to P(Bethany)
B)No, since P(Antonia given Bethany) is not equal to P(Antonia)
C)Yes, since P(Antonia given Bethany) is equal to P(Bethany)
D)Yes, since P(Antonia given Bethany) is equal to P(Antonia)
E)Yes, since P(Bethany given Antonia) is equal to P(Antonia)

Question 70

Your investment club plans to buy three stocks this semester and has narrowed the choice of stocks to a final ten- six US companies and four EU companies.From the ten finalists, you now plan to randomly select the three stocks to buy.What is the probability that you end up buying one US stock and two EU stocks?

A).30
B).80
C).20
D).70
E).25

Question 71

Antonia and Bethany played in the same 50 tennis matches last year.Antonia made the finals in 20 of those matches.Bethany made the finals in 15 of the matches.In 12 of the matches, they both made the final.In what proportion of the matches did neither player make it to the final match?

A).24
B).82
C).90
D).88
E).54

Question 72

K-Tone Marketing has just launched two new products: Product A and Product B.The probability that A will become a market leader is put at .60.The probability that B will become a market leader is .20 of the time.Assuming that the success of one product is independent of the success of the other, what is the probability that at least one of the products will end up being a market leader?

A).68
B).48
C).12
D).32
E).50

Question 73

The price of Chrysler stock increased on 30% of the trading days over the past year.The price of Ford stock increased on 40% of the trading days over the past year.On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well.On what proportion of the days did exactly one of the stocks increase in price?

A).22
B).88
C).40
D).12
E).24

Question 74

Antonia and Bethany played in the same 50 tennis matches last year.Antonia made the finals in 20 of those matches.Bethany made the finals in 15 of the matches.In 12 of the matches, they both made the final.Determine the proportion of the matches in which Bethany made the final, but Antonia did not.

A).10
B).24
C).18
D).06
E).76

Question 75

The price of Chrysler stock increased on 30% of the trading days.The price of Ford stock increased on 40% of the trading days over the past year.On 60% of the days when the price of Ford stock increased, the price of Ford stock increased as well.On what proportion of the days did neither stock increase in price?

A).82
B).46
C).54
D).30
E).88

Question 76

If the probability of an economic recovery next year is 0.55, what is the probability that there won't be a recovery?

A).45
B).25
C).015
D).50
E).75

Question 77

According to studies, 62% percent of online teenagers are Facebook users, while 51% are users of Twitter.If 43% are both Facebook and Twitter users, what proportion of Facebook users are Twitter users?

A).694
B).267
C).733
D).843
E).167

Question 78

If the probability that either the Microsoft or Intel (or both) will have a significant growth in profits next year is 0.75, what is the probability that neither will?

A).25
B).176
C).125
D).15
E).475

Question 79

Your investment club plans to buy three stocks this semester and has narrowed the choice of stocks to a final ten- six US companies and four EU companies.From the ten finalists, you now plan to randomly select the three stocks to buy.Determine the probability that you would end up with all three choices being US stocks.

A).1823
B).2472
C).1667
D).1258
E).2205

Question 80

According to studies, 62% percent of online teenagers are Facebook users, while 51% are users of Twitter.If 43% are both Facebook and Twitter users, what percent of Twitter users are Facebook users?

A).167
B).694
C).733
D).267
E).843