Deck 4: Probability

Question 1

If two events are mutually exclusive, then their joint probability is always zero.

Answer 1

True

Question 2

A joint probability is the probability that at least one of two events occurs.

Answer 2

False

Question 3

The law of multiplication gives the probability that at least one of the two events will occur.

Answer 3

False

Question 4

If two events are mutually exclusive, then the two events are also independent.

Question 5

Given two events, A and B, if the probability of either A or B occurring is 0.6, then the probability of neither A nor B occurring is -0.6.

Question 6

If the occurrence of one event does not affect the occurrence of another event, then the two events are mutually exclusive.

Question 7

An experiment is a process that produces outcomes.

Question 8

The method of assigning probabilities to uncertain outcomes based on laws and rules is called the relative frequency method.

Question 9

The list of all elementary events for an experiment is called the sample space.

Question 10

In the conditional probability of P(E₁|E₂)is when E₂ has occurred and then the probability of E₁ occurring is determined.

Question 11

Given two events, A and B, if the probability of A is 0.7, the probability of B is 0.3, and the joint probability of A and B is 0.21, then the two events are independent.

Question 12

An event that cannot be broken down into other events is called a certainty outcome.

Question 13

Assigning probabilities by dividing the number of ways that an event can occur by the total number of possible outcomes in an experiment is called the classical method.

Question 14

Probability is used to develop knowledge of the fundamental mathematical tools for quantitatively assessing risk.

Question 15

Assigning probabilities to uncertain events based on one's beliefs or intuitions is called classical method.

Question 16

Inferring the value of a population parameter from the statistic on a random sample drawn from the population is an inferential process under uncertainty.

Question 17

If the probability that someone likes the color blue is 44% and the probability that among those individuals, the probability that they wake up early is 52%, then the probability that individuals who like the color blue and wake up early is about 23%.

Question 18

The probability that a person's favorite color is blue would be an example of a marginal probability.

Question 19

The probability of A $\cup$ B where A is receiving a state grant and B is receiving a federal grant is the probability of receiving no more than one of the two grants.

Question 20

If the occurrence of one event precludes the occurrence of another event, then the two events are mutually exclusive.

Question 21

Which of the following statements is not true regarding probabilities:

A)probability is the basis for inferential statistics
B)probabilities are subjective measures with limited value in business.
C)probabilities are used to determine the likelihood of certain outcomes
D)probabilities can inform many business decisions.

Question 22

The list of all elementary events for an experiment is called _______.

A)the sample space
B)the exhaustive list
C)the population space
D)the event union
E)a frame

Question 23

Which of the following is not a legitimate probability value?

A)0.87
B)12/13
C)0.05
D)5/4
E)0.93

Question 24

Assigning probability 1/52 on drawing the ace of spade in a deck of cards is an example of assigning probabilities using the ________________ method

A)subjective probability
B)relative frequency
C)classical probability
D)a priori probability
E)a posterior probability

Question 25

Given that two events, A and B, are independent, if the marginal probability of A is 0.6, the conditional probability of A given B will be 0.4.

Question 26

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are mutually exclusive.

Question 27

If P(X|Y)= P(X)then the events are X and Y are independent.

Question 28

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.The complement of F is ___________.

A){Albert, Betty, Jack, Patty}
B){Betty, Patty, Meagan}
C){Albert, Abel, Jack}
D){Betty, Abel}
E){Meagan}

Question 29

In a set of 12 aluminum castings, two castings are defective (D), and the remaining ten are good (G).A quality control inspector randomly selects three of the twelve castings with replacement to test.The sample space for selecting the group to test contains __________ elementary events.

A)8
B)220
C)120
D)10
E)66

Question 30

Which of the following is a legitimate probability value?

A)1.67
B)16/15
C)-0.23
D)3/2
E)0.28

Question 31

If the probability that someone likes the color blue is 44% and the probability that individuals wake up early is 64%, then the probability that individuals who like the color blue and wake up early is about 23%.In this case, the two events are independent.

Question 32

If X and Y are mutually exclusive events, then if X occurs _______.

A)Y must also occur
B)Y cannot occur
C)X and Y are independent
D)X and Y are complements
E)A and Y are collectively exhaustive

Question 33

In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G).A quality control inspector randomly selects three of the twenty-five castings without replacement, to test.The sample space for selecting the group to test contains ____________ elementary events.

A)12,650
B)2,300
C)455
D)16
E)15,625

Question 34

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F $\cap$ H is ___________.

A){Meagan}
B){Betty, Patty, Abel, Meagan}
C)empty, since F and H are complements
D)empty, since F and H are independent
E)empty, since F and H are mutually exclusive

Question 35

If E and F are mutually exclusive, then _______.

A)the probability of the union is zero
B)P(E)= 1 - P(F)
C)the probability of the intersection is zero
D)the probability of the union is one
E)P(E)= P(F)

Question 36

Given two events A and B each with a non-zero probability, if the conditional probability of A given B is zero, it implies that the events A and B are independent.

Question 37

Bayes' rule is an extension of the law of conditional probabilities to allow revision of original probabilities with new information.

Question 38

Bayes' rule is a rule to assign probabilities under the relative frequency method.

Question 39

Consider the following sample space, S, and several events defined on it.S = {Albert, Betty, Abel, Jack, Patty, Meagan}, and the events are: F = {Betty, Patty, Meagan}, H = {Abel, Meagan}, and P = {Betty, Abel}.F $\cup$ H is ___________.

A){Meagan}
B){Betty, Abel, Patty, Meagan}
C)empty, since F and H are complements
D)empty, since F and H are independent
E)empty, since F and H are mutually exclusive

Question 40

Belinda Bose is reviewing a newly proposed advertising campaign.Based on her 15-years' experience, she believes the campaign has a 75% chance of significantly increasing brand name recognition of the product.This is an example of assigning probabilities using the ________________ method.

A)subjective probability
B)relative frequency
C)classical probability
D)a priori probability
E)a posterior probability

Question 41

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Industry Sector }$
$\begin{array}{|c|c|c|c|c|}\hline \text { Irvestrnent }\\ \text { Objective } & \text { Electronics } & \text { Airlines } & \text { Healthcare } & \text { Total } \\\hline \text { Growth } & 84 & 21 & 35 & 140 \\\hline \text { Income } & 36 &9& 15 &60 \\\hline \text { Total } & 120 & 30 & 50 & 200\\\hline \end{array}$ Which of the following statements is true?

A)Growth and Healthcare are complementary events.
B)Electronics and Growth are independent.
C)Electronics and Growth are mutually exclusive.
D)Airlines and Healthcare are collectively exhaustive.
E)Electronics and Healthcare are collectively exhaustive.

Question 42

If the CEO of Apple wanted to know the probability that someone would own an Apple computer and spend more than 20 hours each week on the internet would be an example of a _____________ probability.

A)unconditional
B)union
C)joint
D)marginal
E)conditional

Question 43

Given P(A)= 0.40, P(B)= 0.50, P(A $\cap$ B)= 0.15.Find P(A $\cup$ B).

A)0.90
B)1.05
C)0.75
D)0.65
E)0.60

Question 44

One event is that individuals like lasagna and the other event is that individuals like soda, the union of these two events would be the probability of _____________.

A)both events occurring
B)at least one event occurring
C)neither event occurring
D)0%
E)100%

Question 45

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year, P (SUV)= ___________. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Buyer Gender }$
$\begin{array}{|r|c|c||c|}\hline \text { Type of }\\ \text { Vehicle } & \text { Female } & \text { Male } & \text { Total } \\\hline \text { SUV } & & & \\\hline \text { Not SUV } & .30 & .40 & \\\hline \text { Total } & &.60& 1.00\\\hline\end{array}$

A)0.30
B)0.40
C)0.12
D)0.10
E)0.60

Question 46

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year, P (Male)= ________ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Buyer Gender }$
$\begin{array}{|r|c|c||c|}\hline \text { Type of }\\ \text { Vehicle } & \text { Female } & \text { Male } & \text { Total } \\\hline \text { SUV } & & & \\\hline \text { Not SUV } & .32 & .48 & \\\hline \text { Total } & .40 & & 1.00\\\hline\end{array}$

A)0.48
B)0.50
C)0.20
D)0.02
E)0.60

Question 47

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Industry Sector }$
$$\begin{array} { | c | c | c | c | c | } \hline \text { Irvestment } & & \\ \text { Objective } & \text { Electronics } & \text { Airlines } & \text { Healthcare } & \text { Total } \\\hline \text { Growth } & 100 & 10 & 40 & 150 \\\hline \text { Income } & 20 & 20 & 10 & 50 \\\hline \text { Total } & 120 & 30 & 50 & 200 \\\hline\end{array}$$ If a stock is selected randomly from Meagan's portfolio, P (Healthcare $\cap$ Electronics)= _______.

A)0.25
B)0.85
C)0.60
D)0.75
E)0.90

Question 48

Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.Find the probability that among all students, a student is in finance and is also in statistics.

A)0.15
B)0.70
C)0.55
D)0.12
E)0.60

Question 49

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Industry Sector }$
$$\begin{array} { | c | c | c | c | c | } \hline \text { Irvestment } & & \\ \text { Objective } & \text { Electronics } & \text { Airlines } & \text { Healthcare } & \text { Total } \\\hline \text { Growth } & 100 & 10 & 40 & 150 \\\hline \text { Income } & 20 & 20 & 10 & 50 \\\hline \text { Total } & 120 & 30 & 50 & 200 \\\hline\end{array}$$ If a stock is selected randomly from Meagan's portfolio, P (Growth)= _______.

A)0.50
B)0.83
C)0.67
D)0.75
E)0.90

Question 50

Max Sandlin researched the characteristics of stock market investors.He found that sixty percent of all investors have a net worth exceeding $1,000,000; 20% of all investors use an online brokerage; and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage.An investor is selected randomly, and E is the event "net worth exceeds $1,000,000" and O is the event "uses an online brokerage." P(O $\cup$ E)= _____________.

A)0.17
B)0.50
C)0.80
D)0.70
E)0.10

Question 51

Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant.Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively.A plant employee is selected randomly; F is the event "works in the finishing department;" and A is the event "is absent excessively." P(A $\cup$ F)= _____________.

A)0.07
B)0.10
C)0.20
D)0.23
E)0.37

Question 52

Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a- finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.Find P(S).

A)0.15
B)0.35
C)0.40
D)0.55
E)0.60

Question 53

The probability of at least one of two events occurring would be an example of a____________ probability.

A)marginal
B)union
C)joint
D)conditional
E)non-union

Question 54

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the following joint probability table that was developed from the dealer's records for the previous year, P (Female)= __________. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Buyer Gender }$
$\begin{array}{|r|c|c||c|}\hline \text { Type of }\\ \text { Vehicle } & \text { Female } & \text { Male } & \text { Total } \\\hline \text { SUV } & & & \\\hline \text { Not SUV } & .30 & .40 & \\\hline \text { Total } & .40 & & 1.00\\\hline\end{array}$

A)0.30
B)0.40
C)0.12
D)0.10
E)0.60

Question 55

The CEO of Apple wanted to know the probability that someone would own an Apple computer or spend more than 20 hours each week on the internet, this would be an example of a ______________ probability.

A)union
B)unconditional
C)marginal
D)conditional
E)joint

Question 56

The number of different committees of 2 students that can be chosen from a group of 5 students is

A)20
B)2
C)5
D)10
E)1

Question 57

Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.A student is randomly selected, what is the probability that the student is enrolled in either finance or statistics or both?

A)0.15
B)0.75
C)0.60
D)0.55
E)0.90

Question 58

If the CEO of Apple wanted to know the probability that if someone owned an Apple computer, they would also own a different brand computer, this would be an example of a __________ probability.

A)conditional
B)marginal
C)joint
D)non-joint
E)union

Question 59

The probability that given one event has occurred that another event would occur would be an example of _________ probability.

A)marginal
B)union
C)joint
D)conditional
E)non-union

Question 60

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Industry Sector }$
$\begin{array}{|c|c|c|c|c|}\hline \text { Irvestrnent }\\ \text { Objective } & \text { Electronics } & \text { Airlines } & \text { Healthcare } & \text { Total } \\\hline \text { Growth } & 100 & 10 & 40 & 150 \\\hline \text { Income } & 20 & 20 & 10 & 50 \\\hline \text { Total } & 120 & 30 & 50 & 200\\\hline \end{array}$ Which of the following statements is not true?

A)Growth and Income are complementary events.
B)Electronics and Growth are dependent.
C)Electronics and Healthcare are mutually exclusive.
D)Airlines and Healthcare are collectively exhaustive.
E)Growth and Income are collectively exhaustive.

Question 61

Suppose that 3% of all TVs made by a company in 2018 are defective.If 2 of these TVs are randomly selected what is the probability that both are defective?

A)0.0009
B)0.0025
C)0.0900
D)0.0475
E)0.19

Question 62

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Find P (A|B).

A)0.45
B)0.135
C)0.30
D)0.111
E)0.167

Question 63

Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant.Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively.A plant employee is selected randomly; F is the event "works in the finishing department;" and A is the event "is absent excessively." P(A|F)= _____________.

A)0.37
B)0.70
C)0.13
D)0.35
E)0.80

Question 64

Given the following joint probability table, find the probability that a dog is small and takes less than 30-minute walks? $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Walk Time }$
$$\begin{array} { | c | c | c | | r | } \hline \text { Type of } & & \\ \text { Dog } & < 30 \mathrm {~min} & \geq 30 \mathrm {~min} & \text { Total } \\\hline \text { Bmall } & .29 & .08 & .36 \\\hline \text { Large } & .22 & .41 & .63 \\\hline \text { Total } & .51 & .49 & 1.00 \\\hline\end{array}$$

A)63%
B)22%
C)29%
D)51%
E)32%

Question 65

Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Plano Power Plant.Ten percent of all plant employees work in the finishing department; 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively.A plant employee is selected randomly; F is the event "works in the finishing department;" and A is the event "is absent excessively." P(F|A)= _____________.

A)0.35
B)0.70
C)0.13
D)0.37
E)0.10

Question 66

A recent survey found that 24% of people in Michigan like oatmeal.If the probability that someone lives in Michigan is 4.8%.What is the probability that you choose two people in the US and they are both from Michigan?

A)28.4%
B)24.0%
C)0.2%
D)100.0%
E)48.0%

Question 67

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labeled A, B, and C.The consumers are classified according to age and package design preference. $$\begin{array} { | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { Total } \\\hline \text { Under 25 years } & 22 & 34 & 40 & 96 \\\hline 25 \text { or older } & 54 & 28 & 22 & 104 \\\hline \text { Total } & 76 & 62 & 62 & 200 \\\hline\end{array}$$ If one of these consumers is randomly selected, what is the probability that the person prefers design A and is under 25?

A)0.22
B)0.11
C)0.18
D)0.54
E)0.78

Question 68

The table below provides summary information about the students in a class.The sex of each individual and their age is given. $$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Fernale } & \text { Total } \\\hline \text { Under 20 yrs old } & 10 & 8 & 18 \\\hline \begin{array} { l } \text { Between } 20 \text { and } 25 \\\text { yrs old }\end{array} & 12 & 18 & 30 \\\hline \text { Older tharn 25 yrs. } & 26 & 26 & 52 \\\hline \text { Total } & 48 & 52 & 100 \\\hline\end{array}$$ If a student is randomly selected from this group, what is the probability that the student is a female who is also under 20 years old?

A)0.08
B)0.18
C)0.52
D)0.26
E)0.78

Question 69

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Which of the following is true?

A)A and B are independent
B)A and B are mutually exclusive
C)A and B are collectively exhaustive
D)A and B are not independent
E)A and B are complimentary

Question 70

A recent survey found that 24% of people in Michigan like oatmeal.If the probability that someone lives in Michigan is 4.8%, what is the probability that someone lives in Michigan and likes oatmeal?

A)28.4%
B)24.0%
C)4.8%
D)19.2%
E)1.2%

Question 71

It is known that 20% of all students in some large university are overweight, 20% exercise regularly and 2% are overweight and exercise regularly.What is the probability that a randomly selected student is either overweight or exercises regularly or both?

A)0.40
B)0.38
C)0.20
D)0.42
E)0.10

Question 72

Given P (A)= 0.45, P (B)= 0.30, P (A $\cap$ B)= 0.05.Find P (B|A).

A)0.45
B)0.135
C)0.30
D)0.111
E)0.167

Question 73

Meagan Dubean manages a portfolio of 200 common stocks.Her staff classified the portfolio stocks by 'industry sector' and 'investment objective.' $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Industry Sector }$
$$\begin{array} { | c | c | c | c | c | } \hline \text { Irvestment } & & \\ \text { Objective } & \text { Electronics } & \text { Airlines } & \text { Healthcare } & \text { Total } \\\hline \text { Growth } & 100 & 10 & 40 & 150 \\\hline \text { Income } & 20 & 20 & 10 & 50 \\\hline \text { Total } & 120 & 30 & 50 & 200 \\\hline\end{array}$$
If a stock is selected randomly from Meagan's portfolio, P (Airlines|Income)= _______.

A)0.10
B)0.40
C)0.25
D)0.67
E)0.90

Question 74

An automobile dealer wishes to investigate the relation between the gender of the buyer and type of vehicle purchased.Based on the joint probability table below that was developed from the dealer's records for the previous year, P (Female $\cap$ SUV)= _______. $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$$\text { Buyer Gender }$
$\begin{array}{|r|c|c||c|}\hline \text { Type of }\\ \text { Vehicle } & \text { Female } & \text { Male } & \text { Total } \\\hline \text { SUV } & & & \\\hline \text { Not SUV } & .30 & .40 & \\\hline \text { Total } & &.60 & 1.00\\\hline\end{array}$

A)0.30
B)0.40
C)0.12
D)0.10
E)0.60

Question 75

Suppose 5% of the population have a certain disease.A laboratory blood test gives a positive reading for 95% of people who have the disease.What is the probability of testing positive and having the disease?

A)0.0475
B)0.95
C)0.05
D)0.9
E)0.02

Question 76

Let F be the event that a student is enrolled in a finance course, and let S be the event that a student is enrolled in a statistics course.It is known that 40% of all students are enrolled in a finance course and 35% of all students are enrolled in statistics.Included in these numbers are 15% who are enrolled in both statistics and finance.A student is randomly selected, and it is found that the student is enrolled in finance.What is the probability that this student is also enrolled in statistics?

A)0.15
B)0.75
C)0.375
D)0.50
E)0.80

Question 77

The table below provides summary information about the students in a class.The sex of each individual and their age is given. $$\begin{array} { | l | c | c | c | } \hline & \text { Male } & \text { Fernale } & \text { Total } \\\hline \text { Under 20 yrs old } & 10 & 8 & 18 \\\hline \begin{array} { l } \text { Between } 20 \text { and } 25 \\\text { yrs old }\end{array} & 12 & 18 & 30 \\\hline \text { Older tharn 25 yrs. } & 26 & 26 & 52 \\\hline \text { Total } & 48 & 52 & 100 \\\hline\end{array}$$ If a student is randomly selected from this group, what is the probability that the student is male?

A)0.12
B)0.48
C)0.50
D)0.52
E)0.68

Question 78

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labeled A, B, and C.The consumers are classified according to age and package design preference. $$\begin{array} { | c | c | c | c | c | } \hline & \text { A } & \text { B } & \text { C } & \text { Total } \\\hline \text { Under 25 years } & 22 & 34 & 40 & 96 \\\hline 25 \text { or older } & 54 & 28 & 22 & 104 \\\hline \text { Total } & 76 & 62 & 62 & 200 \\\hline\end{array}$$ If one of these consumers is randomly selected, what is the probability that the person prefers design A?

A)0.76
B)0.38
C)0.33
D)0.22
E)0.39

Question 79

A recent survey found that 24% of people in Michigan like oatmeal.If the probability that someone lives in Michigan is 4.8%.What is the probability that two people from Michigan would both like oatmeal?

A)5.8%
B)24.0%
C)4.8%
D)48.0%
E)1.2%

Question 80

Max Sandlin is exploring the characteristics of stock market investors.He found that sixty percent of all investors have a net worth exceeding $1,000,000; 20% of all investors use an online brokerage; and 10% of all investors a have net worth exceeding $1,000,000 and use an online brokerage.An investor is selected randomly, and E is the event "net worth exceeds $1, 000, 000," and O is the event "uses an online brokerage." P(O|E)= _____________.

A)0.17
B)0.50
C)0.80
D)0.70
E)0.88