Deck 4: Basic Probability

Question 1

The numerical value that represents the likelihood that a particular event will occur is its_____________ .

Answer 1

probability

Question 2

The closing price of a company's stock tomorrow can be lower,higher or the same as today's closing price.Based on the closing price of the stock collected over the last month,25% of the days the closing price was higher than previous day's closing price,45% was lower than previous day's and 30% was the same as previous day's.Based on this information,the probability that tomorrow's closing price will be higher than today's is 25%.This is an example of using which of the following probability approach?

A) A priori probability.
B) Empirical probability.
C) Subjective probability.
D) Conditional probability.

Answer 2

B

Question 3

The closing price of a company's stock tomorrow can be lower,higher or the same as today's closing price.After evaluating all the information available on the company's fundamentals and the economic environment,the probability that tomorrow's closing price will be higher than today's is determined to be 25%.This is an example of using which of the following probability approach?

A) A priori probability.
B) Empirical probability.
C) Subjective probability.
D) Conditional probability.

Answer 3

C

Question 4

All the events in the sample space that are not part of the specified event are called

A) simple events.
B) the complement of the event.
C) the sample space.
D) joint events.

Question 5

An event that cannot occur is an impossible event.

Question 6

Empirical classical probability is objective probability obtained from the relative frequency of occurrence of an event.

Question 7

The probability of an occurrence described by two or more characteristics is known as marginal probability.

Question 8

_____________ probability differs from person to person.

A) Marginal
B) A priori classical
C) Empirical classical
D) Subjective

Question 9

The _____________ includes all simple outcomes not in an event.

A) random experiment
B) sample space
C) compliment
D) joint probability

Question 10

Priori classical probability is based on observed data.

Question 11

The closing price of a company's stock tomorrow can be lower,higher or the same as today's closing price.Without any prior information that may affect the price of the stock tomorrow,the probability that it will close higher than today's close is 1/3.This is an example of using which of the following probability approach?

A) A priori probability.
B) Empirical probability.
C) Subjective probability.
D) Conditional probability.

Question 12

If an event has a probability of 1,then it is a(n)_____________ .

A) impossible event
B) certain event
C) probable event
D) simple event

Question 13

Simple probability is also called

A) Bayes' theorem.
B) joint probability.
C) marginal probability.
D) conditional probability.

Question 14

To graphically represent various events as unions and intersections,one should use a contingency table.

Question 15

The collection of all simple events of a random experiment is called

A) a simple probability.
B) a sample space.
C) the null set.
D) a joint probability.

Question 16

To represent a sample space for joint events classified by two characteristics,one should use a cross-classification table.

Question 17

The collection of all the possible events is called a sample space.

Question 18

A complement of an event B (B')includes all events not included in event B.
B. False

Question 19

Objective probability obtained from the relative frequency of occurrence of an event is known as empirical classical probability.

Question 20

A random experiment is a precisely described scenario that leads to an outcome that can be predicted with certainty.

Question 21

If P(A)= 0.4 and P(B)= 0.6,then A and B must be mutually exclusive.

Question 22

If P(A and B)= 1,then A and B must be collectively exhaustive.

Question 23

If P(A or B)= 1,then A and B must be mutually exclusive.

Question 24

If P(A and B)= 0,then A and B must be collectively exhaustive.

Question 25

If P(A or B)= 1,then A and B must be collectively exhaustive.

Question 26

If two events are mutually exclusive and collectively exhaustive,what is the probability that one or the other occurs?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 27

If two events are mutually exclusive and collectively exhaustive,what is the probability that both occur?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 28

If either A or B must occur they are called collectively exhaustive.

Question 29

If two events are collectively exhaustive,what is the probability that one or the other occurs?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 30

If two events are collectively exhaustive,what is the probability that both occur at the same time?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 31

If two events are mutually exclusive,what is the probability that one or the other occurs?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 32

If two events are mutually exclusive,what is the probability that both occur at the same time?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 33

If P(A and B)= 1,then A and B must be mutually exclusive.

Question 34

If either A or B must occur they are called mutually exclusive.

Question 35

If P(A)= 0.4 and P(B)= 0.6,then A and B must be collectively exhaustive.

Question 36

If A and B cannot occur at the same time they are called mutually exclusive.

Question 37

When A and B are mutually exclusive,P(A or B)can be found by adding P(A)and P(B).

Question 38

If two equally likely events A and B are mutually exclusive and collectively exhaustive,what is the probability that event A occurs?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 39

If P(A and B)= 0,then A and B must be mutually exclusive.

Question 40

If events A and B are mutually exclusive and collectively exhaustive,what is the probability that event A occurs?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 41

If event A and event B cannot occur at the same time,then events A and B are said to be

A) collectively exhaustive.
B) statistically independent.
C) mutually exclusive.
D) None of the above.

Question 42

The employees of a company were surveyed on questions regarding their educational background and marital status.Of the 600 employees,400 had university degrees,100 were single,and 60 were single university graduates.

- The probability that an employee of the company does not have a university degree is

A) 0.33.
B) 0.75.
C) 0.67.
D) 0.10.

Question 43

The probability that a new advertising campaign will increase sales is estimated to be 0.80.The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40.

-Assuming that the two events are independent,the probability that the cost is kept within budget or the campaign will increase sales is

A) 0.68.
B) 0.88.
C) 0.32.
D) 0.20.

Question 44

The probability that house sales will increase in the next six months is estimated to be 0.25.The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74.The probability that house sales or interest rates will go up during the next six months is estimated to be 0.89.

- The events of 'increase in house sales' and 'increase in interest rates' in the next six months are

A) collectively exhaustive.
B) mutually exclusive.
C) statistically independent.
D) None of the above.

Question 45

The probability that house sales will increase in the next six months is estimated to be 0.25.The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74.The probability that house sales or interest rates will go up during the next six months is estimated to be 0.89.

- The probability that house sales will increase but interest rates will not increase during the next six months is

A) 0.065.
B) 0.51.
C) 0.89.
D) 0.15.

Question 46

A company has two machines that produce widgets.An older machine produces 23% defective widgets,while the new machine produces only 8% defective widgets.In addition,the new machine produces three times as many widgets as the older machine does.What is the probability that a randomly chosen widget produced by the company is defective?

A) 0.1175
B) 0.078
C) 0.156
D) 0.310

Question 47

The employees of a company were surveyed on questions regarding their educational background and marital status.Of the 600 employees,400 had university degrees,100 were single,and 60 were single university graduates.

- The probability that an employee of the company is married and has a university degree is

A) 340/600.
B) 500/600.
C) 400/600.
D) 40/600.

Question 48

The probability that house sales will increase in the next six months is estimated to be 0.25.The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74.The probability that house sales or interest rates will go up during the next six months is estimated to be 0.89.

- The events of 'increase in house sales' and 'no increase in house sales' in the next six months are

A) statistically independent.
B) collectively exhaustive.
C) mutually exclusive.
D) Both B and C.

Question 49

The probability that house sales will increase in the next six months is estimated to be 0.25.The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74.The probability that house sales or interest rates will go up during the next six months is estimated to be 0.89.

- The probability that neither house sales nor interest rates will increase during the next six months is

A) 0.11.
B) 0.90.
C) 0.195.
D) 0.89.

Question 50

A business venture can result in the following outcomes (with their corresponding chance of occurring in brackets): Highly Successful (10%),Successful (25%),Break Even (25%),Disappointing (20%),and Highly Disappointing (?).If these are the only outcomes possible for the business venture,what is the chance that the business venture will be considered Highly Disappointing?

A) 20%
B) 15%
C) 10%
D) 25%

Question 51

According to a survey of Australian households,the probability that the residents own two cars if annual household income is over $50,000 is 80%.Of the households surveyed,60% had incomes over $50,000 and 70% had two cars.

- The probability that the residents of a household do not own two cars and have an income over $50,000 a year is

A) 0.12.
B) 0.18.
C) 0.22.
D) 0.48.

Question 52

The probability that house sales will increase in the next six months is estimated to be 0.25.The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74.The probability that house sales or interest rates will go up during the next six months is estimated to be 0.89.

-The probability that both house sales and interest rates will increase during the next six months is

A) 0.705.
B) 0.90.
C) 0.185.
D) 0.10.

Question 53

According to a survey of Australian households,the probability that the residents own two cars if annual household income is over $50,000 is 80%.Of the households surveyed,60% had incomes over $50,000 and 70% had two cars.

- The probability that the residents of a household own two cars and have an income less than or equal to $50,000 a year is

A) 0.12.
B) 0.18.
C) 0.22.
D) 0.48.

Question 54

The employees of a company were surveyed on questions regarding their educational background and marital status.Of the 600 employees,400 had university degrees,100 were single,and 60 were single university graduates.

-The probability that an employee of the company is single or has a university degree is

A) 0.25.
B) 0.667.
C) 0.733.
D) 0.10.

Question 55

A recent survey of banks revealed the following distribution for the interest rate being charged on a home loan (based on a 30-year mortgage with a 10% down payment). $$\begin{array} { | l | c | c | c | c | c | } \hline \text { Interest Rate } & 7.0 \% & 7.5 \% & 8.0 \% & 8.5 \% & > 8.5 \% \\\hline \text { Probability } & 0.12 & 0.23 & 0.24 & 0.35 & 0.06 \\\hline\end{array}$$ If a bank is selected at random from this distribution,what is the chance that the interest rate charged on a home loan will exceed 8.0%?

A) 0.59
B) 0.06
C) 1.00
D) 0.41

Question 56

If either event A or event B must occur,then events A and B are said to be

A) collectively exhaustive.
B) mutually exclusive.
C) statistically independent.
D) None of the above.

Question 57

According to a survey of Australian households,the probability that the residents own two cars if annual household income is over $50,000 is 80%.Of the households surveyed,60% had incomes over $50,000 and 70% had two cars.

-The probability that the residents of a household own two cars and have an income over $50,000 a year is

A) 0.12.
B) 0.18.
C) 0.22.
D) 0.48.

Question 58

If two equally likely events A and B are collectively exhaustive,what is the probability that event A occurs?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 59

The probability that a new advertising campaign will increase sales is estimated to be 0.80.The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40.

- Assuming that the two events are independent,the probability that the cost is not kept within budget or the campaign will not increase sales is

A) 0.12.
B) 0.68.
C) 0.32.
D) 0.88.

Question 60

If two equally likely events A and B are mutually exclusive,what is the probability that event A occurs?

A) 0
B) 0.50
C) 1.00
D) Cannot be determined from the information given.

Question 61

Instruction 4.2
An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained.
$$\begin{array} { | l | l | l | } \hline & \text { Did Well on Exam } & \text { Did Poorly on Exam } \\\hline \text { Studying for Exam } & 80 & 20 \\\hline \text { Went to a pub } & 30 & 70 \\\hline\end{array}$$

-Referring to Instruction 4.2,what is the probability that a randomly selected student who went to a pub will do well on the exam?

A) 30/100 or 30%
B) (100/200) * (110/200) or 27.50%
C) 30/200 or 15%
D) 30/110 or 27.27%

Question 62

A survey is taken among customers of fast-food restaurants to determine preference for hamburgers or chicken. Of 200 respondents selected, 75 were children and 125 were adults. One hundred and twenty preferred hamburgers and 80 preferred chicken. Fifty-five of the children preferred hamburgers.

-Referring to Instruction 4.3,the probability that a randomly selected individual is an adult or a child is _____________ .

Question 63

Instruction 4.1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Referring to Instruction 4.1,what proportion of accidents involved more than one vehicle?

A) 75/400 or 18.75%
B) 325/400 or 81.25%
C) 50/400 or 12.5%
D) 275/400 or 68.75%

Question 64

Suppose A and B are mutually exclusive events where P(A)= 0.4 and P(B)= 0.5.Then P(A or B)= _____________ .

Question 65

Instruction 4.1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Referring to Instruction 4.1,given that multiple vehicles were involved,what proportion of accidents involved alcohol?

A) 120/230 or 52.17%
B) 120/170 or 70.59%
C) 120/325 or 36.92%
D) 120/400 or 30%

Question 66

You know that the probability of a randomly selected student will cheat on an exam is 1%.You also know that the probability of a randomly selected student will cheat on an exam knowing that his/her fellow classmate is cheating on the exam is also 1%.Which of the following is true about the event of 'the randomly selected student cheating on an exam' and 'his/her classmate is cheating on the exam'?

A) They are mutually exclusive.
B) They are independent.
C) They are collectively exhaustive.
D) None of the above.

Question 67

Instruction 4.2
An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained.
$$\begin{array} { | l | l | l | } \hline & \text { Did Well on Exam } & \text { Did Poorly on Exam } \\\hline \text { Studying for Exam } & 80 & 20 \\\hline \text { Went to a pub } & 30 & 70 \\\hline\end{array}$$

-Referring to Instruction 4.2,the events 'Did Well on Exam' and 'Did Poorly on Exam' are

A) statistically dependent.
B) collective exhaustive.
C) mutually exclusive.
D) All of the above.

Question 68

Instruction 4.1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Referring to Instruction 4.1,given that three vehicles were involved,what proportion of accidents involved alcohol?

A) 20/170 or 11.77%
B) 20/50 or 40%
C) 20/400 or 5%
D) 20/30 or 66.67%

Question 69

Suppose A and B are mutually exclusive events where P(A)= 0.4 and P(B)= 0.5.Then P(A and B)= _____________ .

Question 70

Instruction 4.2
An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained.
$$\begin{array} { | l | l | l | } \hline & \text { Did Well on Exam } & \text { Did Poorly on Exam } \\\hline \text { Studying for Exam } & 80 & 20 \\\hline \text { Went to a pub } & 30 & 70 \\\hline\end{array}$$

-Referring to Instruction 4.2,the events 'Did Well on Exam' and 'Studying for Exam' are

A) not statistically dependent.
B) collective exhaustive.
C) not mutually exclusive.
D) None of the above.

Question 71

Instruction 4.2
An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained.
$$\begin{array} { | l | l | l | } \hline & \text { Did Well on Exam } & \text { Did Poorly on Exam } \\\hline \text { Studying for Exam } & 80 & 20 \\\hline \text { Went to a pub } & 30 & 70 \\\hline\end{array}$$

-Referring to Instruction 4.2,the events 'Did Well on Exam' and 'Studying for Exam' are

A) statistically dependent.
B) collective exhaustive.
C) mutually exclusive.
D) None of the above.

Question 72

A survey is taken among customers of fast-food restaurants to determine preference for hamburgers or chicken. Of 200 respondents selected, 75 were children and 125 were adults. One hundred and twenty preferred hamburgers and 80 preferred chicken. Fifty-five of the children preferred hamburgers.

-Referring to Instruction 4.3,the probability that a randomly selected individual is an adult is _____________ .

Question 73

Instruction 4.1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Referring to Instruction 4.1,what proportion of accidents involved alcohol and a single vehicle?

A) 50/400 or 12.5%
B) 195/400 or 48.75%
C) 245/400 or 61.25%
D) 25/400 or 6.25%

Question 74

Instruction 4.1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Referring to Instruction 4.1,given that alcohol was not involved,what proportion of the accidents were single vehicle?

A) 25/75 or 33.33%
B) 50/170 or 29.41%
C) 50/75 or 66.67%
D) 25/230 or 10.87%

Question 75

Instruction 4.1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Referring to Instruction 4.1,given alcohol was involved,what proportion of accidents involved a single vehicle?

A) 120/400 or 30%
B) 120/170 or 70.59%
C) 50/170 or 29.41%
D) 50/75 or 66.67%

Question 76

Instruction 4.1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Referring to Instruction 4.1,given that alcohol was not involved,what proportion of the accidents were multiple vehicle?

A) 50/170 or 29.41%
B) 120/170 or 70.59%
C) 25/230 or 10.87%
D) 205/230 or 89.13%

Question 77

Suppose A and B are events where P(A)= 0.4,P(B)= 0.5,and P(A and B)= 0.1.Then P(A or B)= _____________ .

Question 78

Instruction 4.2
An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained.
$$\begin{array} { | l | l | l | } \hline & \text { Did Well on Exam } & \text { Did Poorly on Exam } \\\hline \text { Studying for Exam } & 80 & 20 \\\hline \text { Went to a pub } & 30 & 70 \\\hline\end{array}$$

-Referring to Instruction 4.2,what is the probability that a randomly selected student did well on the exam and also went to a pub on the weekend before the exam?

A) 30/200 or 15%
B) (30 + 70) / 200 or 50%
C) (80 + 30 + 70) / 200 or 90%
D) (80 + 30) / 200 or 55%

Question 79

Instruction 4.1
Mothers Against Drunk Driving is a very visible group whose main focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasised the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analysed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are shown below:

Referring to Instruction 4.1,what proportion of accidents involved alcohol or a single vehicle?

A) 245/400 or 61.25%
B) 195/400 or 48.75%
C) 50/400 or 12.5%
D) 25/400 or 6.25%

Question 80

Instruction 4.2
An alcohol awareness task force at a large Australian university sampled 200 students after the final exam to ask them whether they went out to a pub on the weekend before the exam or spent the weekend studying, and whether they did well or poorly on the exam. The following result was obtained.
$$\begin{array} { | l | l | l | } \hline & \text { Did Well on Exam } & \text { Did Poorly on Exam } \\\hline \text { Studying for Exam } & 80 & 20 \\\hline \text { Went to a pub } & 30 & 70 \\\hline\end{array}$$

-Referring to Instruction 4.2,what is the probability that a randomly selected student did well on the exam or went to a pub on the weekend before the exam?

A) (80 + 30 + 70) / 200 or 90%
B) 30/200 or 15%
C) (80 + 30) / 200 or 55%
D) (30 + 70) / 200 or 50%