Question 1

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

Accepted Answer

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

Question 2

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:
 $$\begin{array} { | c | c | c | c | c | } 
\hline &  { \text { Number of Vehicles involved } } & \
\hline \text { Did alcohol play a role? } & \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } & \text { Totals } \
\hline \text { Yes } & 50 & 100 & 20 & 170 \
\hline \text { No } & 25 & 175 & 30 & 230 \
\hline \text { Totals } & 75 & 275 & 50 & 400 \
\hline
\end{array}$$
-Referring to Instruction 4-1,given alcohol was involved,what proportion of accidents involved a single vehicle?

Accepted Answer

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

Question 3

According to a survey of Australian households,the probability that the residents own 2 cars if annual household income is over $50,000 is 80%.Of the households surveyed,60% had incomes over $50,000 and 70% had 2 cars.The probability that the residents of a household do not own 2 cars and have an income over $50,000 a year is

Accepted Answer

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

Question 4

Instruction 4-5
In a meat packaging plant,Machine A accounts for 60% of the plant's output,while Machine B accounts for 40% of the plant's output.In total,4% of the packages are improperly sealed.Also,3% of the packages are from Machine A and are improperly sealed.
-Referring to Instruction 4-5,if a package is selected at random,the probability that it will be properly sealed is ________.

Accepted Answer

The answer of Instruction 4-5
In a meat packaging plant,Machine A...

Question 5

The collection of all possible events is called

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

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

Accepted Answer

A) True 
 B)False

Question 8

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?

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

The probability that house sales will increase in the next 6 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 6 months is estimated to be 0.89.The probability that house sales will increase but interest rates will not increase during the next 6 months is

Accepted Answer

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

Question 11

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

Accepted Answer

A) True 
 B)False

Question 12

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?

Accepted Answer

A) 30/200 or 15% 
B) (30 + 70)/ 200 or 50% 
C) (80 + 30 + 70)/ 200 or 90% 
D) (80 + 30)/ 200 or 55% 
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 13

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

Accepted Answer

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

Question 14

Instruction 4-4
Suppose that patrons of a restaurant were asked whether they preferred beer or whether they preferred wine.70% said that they preferred beer.60% of the patrons were male.80% of the males preferred beer.
-Referring to Instruction 4-4,suppose a randomly selected patron prefers beer.Then the probability the patron is a male is ________.

Accepted Answer

The answer of Instruction 4-4
Suppose that patrons of a restaurant...

Question 15

Instruction 4-7
A lottery will have the following payoffs possible with their associated probabilities.
 $$\begin{array} { r c } 
{ \text { Payoff } } &  \text { Probability } \
\hline
\$ 200 & 0.0500 \
\$ 25.00 & 0.0100 \
\$ 100.00 & 0.0050 \
\$ 500.00 & 0.0010 \
\$ 5,000.00 & 0.0005 \
\$ 10,000.00 & 0.0001

\end{array}$$ You buy a single ticket.
-Referring to Instruction 4-7,the probability that you win any money is ________.

Accepted Answer

The answer of Instruction 4-7
A lottery will have the following...

Question 16

Instruction 4-6
At a NSW University,60% of the students are from NSW,30% are from interstate,and the remaining 10% are from overseas.All students must take and pass an English Proficiency Test (EPT)before they graduate.60% of the NSW students have passed the EPT,70% of the interstate students have passed the EPT,and 90% of the overseas students have passed the EPT.
-Referring to Instruction 4-6,if a randomly selected student has passed the EPT,the probability the student is from overseas is ________.

Accepted Answer

The answer of Instruction 4-6
At a NSW University,60% of the...

Question 17

Instruction 4-9
A sample of 300 adults is selected.The contingency table below shows their registration status and their preferred source of information on current events.
 $$\begin{array} { | l | c | c | c | c | c | } 
\hline { } &&  { \text { Preferred source of information } } \
\hline{ } && \text { Television } & \text { Newspapers } & \text { Radio } & \text { Internet } \
\hline \text { Voting registration status } & \text { Registered } & 45 & 30 & 45 & 36 \
\hline & \text { Not registered } & 35 & 44 & 45 & 20 \
\hline
\end{array}$$
-Referring to Instruction 4-9,if an adult is selected at random,what is the probability that he/she is a registered voter who prefers to get his/her current information from the television?

Accepted Answer

45/300 = 0

Question 18

If you want to use Bayes' theorem to calculate P(B|A),the numerator of the statistic will be

Accepted Answer

Question 19

Instruction 4-7
A lottery will have the following payoffs possible with their associated probabilities.
 $$\begin{array} { r c } 
{ \text { Payoff } } &  \text { Probability } \
\hline
\$ 200 & 0.0500 \
\$ 25.00 & 0.0100 \
\$ 100.00 & 0.0050 \
\$ 500.00 & 0.0010 \
\$ 5,000.00 & 0.0005 \
\$ 10,000.00 & 0.0001

\end{array}$$ You buy a single ticket.
-Referring to Instruction 4-7,the probability that you win at least $100.00 is ________.

Accepted Answer

The answer of Instruction 4-7
A lottery will have the following...

Question 20

The probability that house sales will increase in the next 6 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 6 months is estimated to be 0.89.The events of "increase in house sales" and "no increase in house sales" in the next 6 months are

Accepted Answer

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

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

The collection of all possible events is called

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

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

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

If you want to use Bayes' theorem to calculate P(B|A),the numerator of the statistic will be

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

Filters

Exam 4: Basic Probability

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

The collection of all possible events is called

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

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

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

If you want to use Bayes' theorem to calculate P(B|A),the numerator of the statistic will be

Introduction and Data Collection

Presenting Data in Tables and Charts

Numerical Descriptive Measures

Some Important Discrete Probability Distributions

The Normal Distribution and Other Continuous Distributions

Sampling Distributions

Confidence Interval Estimation

Fundamentals of Hypothesis Testing: One-Sample Tests

Hypothesis Testing: Two Sample Tests

Analysis of Variance

Simple Linear Regression

Introduction to Multiple Regression

Time-Series Forecasting and Index Numbers

Chi-Square Tests

Multiple Regression Model Building

Decision Making

Statistical Applications in Quality and Productivity Management

Further Non-Parametric Tests

Filters