Question 1

If two events are mutually exclusive, then their intersection

Accepted Answer

A)  will be equal to zero 
B)  can have any value larger than zero 
C)  must be larger than zero, but less than one 
D)  will be one 
A)  will be equal to zero 
B)  can have any value larger than zero 
C)  must be larger than zero, but less than one 
D)  will be one

Question 2

A government agency has 6,000 employees. The employees were asked whether they preferred a four-day work week 10 hours per day), a five-day work week 8 hours per day), or flexible hours. You are given information on the employees' responses broken down by sex.
 $\begin{array}{l|rr|r} 
& \text { Male } & \text { Female } & \text { Total } \
\hline \text { Four days } & 300 & 600 & 900 \
\text { Five days } & 1,200 & 1,500 & 2,700\\text { Flexible } & 300 & 2,100 & 2,400 \
\hline \text { Total } & 1,800 & 4,200 & 6,000
\end{array}$ 
a. What is the probability that a randomly selected employee is a man and is in favor of a four-day work week?
b. What is the probability that a randomly selected employee is female?
c. A randomly selected employee turns out to be female. Compute the probability that she is in favor of flexible hours.
d. What percentage of employees is in favor of a five-day work week?
e. Given that a person is in favor of flexible time, what is the probability that the person is female?
f. What percentage of employees is male and in favor of a five-day work week?

Accepted Answer

a. 0.05
b.

Question 3

Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is

Accepted Answer

A)  one 
B)  any positive value 
C)  zero 
D)  any value between 0 to 1 
A)  one 
B)  any positive value 
C)  zero 
D)  any value between 0 to 1

Question 4

In a horse race, nine horses are running. Assume you have purchased a Trifecta ticket. In Trifecta, the player selects three horses as first, second, and third place winners. To win, those three horses must finish the race in the precise order the player has selected.) How many possibilities of a Trifecta exist?

Accepted Answer

The answer of In a horse race, nine horses are...

Question 5

One of the basic requirements of probability is

Accepted Answer

A)  for each experimental outcome Ei, we must have PEi) ≥ 1 
B)  P
A)  = PAc) - 1 
C)  if there are k experimental outcomes, then ∑PEi) = 1 
D)  ∑PEi) ≥ 1 
A)  for each experimental outcome Ei, we must have PEi) ≥ 1 
B)  P
A)  = PAc) - 1 
C)  if there are k experimental outcomes, then ∑PEi) = 1 
D)  ∑PEi) ≥ 1

Question 6

Any process that generates well-defined outcomes is

Accepted Answer

A)  an event 
B)  an experiment 
C)  a sample point 
D)  a sample space 
A)  an event 
B)  an experiment 
C)  a sample point 
D)  a sample space

Question 7

In a city, 60% of the residents live in houses and 40% of the residents live in apartments. Of the people who live in houses, 20% own their own business. Of the people who live in apartments, 10% own their own business. If a person owns his or her own business, find the probability that he or she lives in a house.

Accepted Answer

The answer of In a city, 60% of the residents...

Question 8

All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee's last name, followed by four numbers.
a. How many possible different ID numbers are there?
b. How many possible different ID numbers are there for employees whose last name starts with an A?

Accepted Answer

a. 260,000

Question 9

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

Accepted Answer

A)  mutually exclusive events 
B)  the intersection of two events 
C)  the union of two events 
D)  conditional events 
A)  mutually exclusive events 
B)  the intersection of two events 
C)  the union of two events 
D)  conditional events

Question 10

A machine is used in a production process. From past data, it is known that 97% of the time the machine is set up correctly. Furthermore, it is known that if the machine is set up correctly, it produces 95% acceptable non- defective) items. However, when it is set up incorrectly, it produces only 40% acceptable items.
a. An item from the production line is selected. What is the probability that the selected item is non-defective?
b. Given that the selected item is non-defective, what is the probability that the machine is set up correctly?

Accepted Answer

The answer of A machine is used in a production...

Question 11

Bayes' theorem is used to compute

Accepted Answer

A)  the prior probabilities 
B)  the union of events 
C)  intersection of events 
D)  the posterior probabilities 
A)  the prior probabilities 
B)  the union of events 
C)  intersection of events 
D)  the posterior probabilities

Question 12

Assume you are taking two courses this semester A and B). The probability that you will pass course A is 0.835, the probability that you will pass both courses is 0.276. The probability that you will pass at least one of the courses is 0.981.
a. What is the probability that you will pass course B?
b. Is the passing of the two courses independent events? Use probability information to justify your answer.
c. Are the events of passing the courses mutually exclusive? Explain.

Accepted Answer

a. 0.422
b. No, PA |

Question 13

If PA) = 0.7, PB) = 0.6, PA ∩ B) = 0, then events A and B are

Accepted Answer

A)  not mutually exclusive 
B)  mutually exclusive 
C)  independent events 
D)  complements of each other 
A)  not mutually exclusive 
B)  mutually exclusive 
C)  independent events 
D)  complements of each other

Question 14

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

Accepted Answer

A)  permutation 
B)  combination 
C)  multiple step experiment 
D)  None of these alternatives is correct. 
A)  permutation 
B)  combination 
C)  multiple step experiment 
D)  None of these alternatives is correct.

Question 15

The probability of an economic decline in the year 2008 is 0.23. There is a probability of 0.64 that we will elect a republican president in the year 2008. If we elect a republican president, there is a 0.35 probability of an economic decline. Let "D" represent the event of an economic decline, and "R" represent the event of election of a Republican president.
a. Are "R" and "D" independent events?
b. What is the probability of a Republican president and economic decline in the year 2008?
c. If we experience an economic decline in the year 2008, what is the probability that there will a Republican president?
d. What is the probability of economic decline or a Republican president in the year 2008? Hint: You want to find PD ∪ R).

Accepted Answer

a. No, because PD) ≠

Question 16

An automobile dealer has kept records on the customers who visited his showroom. Forty percent of the people who visited his dealership were female. Furthermore, his records show that 35% of the females who visited his dealership purchased an automobile, while 20% of the males who visited his dealership purchased an automobile. Let
A1 = the event that the customer is female A2 = the event that the customer is male
a. What is the probability that a customer entering the showroom will buy an automobile?
b. A car salesperson has just informed us that he sold a car to a customer. What is the probability that the customer was female?

Accepted Answer

The answer of An automobile dealer has kept records on...

Question 17

Events A and B are mutually exclusive if their joint probability is

Accepted Answer

A)  larger than 1 
B)  less than zero 
C)  zero 
D)  infinity 
A)  larger than 1 
B)  less than zero 
C)  zero 
D)  infinity

Question 18

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

Accepted Answer

A)  smaller than the probability of tails 
B)  larger than the probability of tails 
C)  1/16 
D)  1/2 
A)  smaller than the probability of tails 
B)  larger than the probability of tails 
C)  1/16 
D)  1/2

Question 19

If PA) = 0.45, PB) = 0.55, and PA ∪ B) = 0.78, then PA | B) =

Accepted Answer

A)  zero 
B)  0.45 
C)  0.22 
D)  0.40 
A)  zero 
B)  0.45 
C)  0.22 
D)  0.40

Question 20

If X and Y are independent events with PX) = 0.90 and PY) = 0.70, then PX∩Y) =

Accepted Answer

A)  0.63 
B)  0.95 
C)  0.20 
D)  1.60 
A)  0.63 
B)  0.95 
C)  0.20 
D)  1.60

If two events are mutually exclusive, then their intersection

Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is

One of the basic requirements of probability is

Any process that generates well-defined outcomes is

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

Bayes' theorem is used to compute

If PA) = 0.7, PB) = 0.6, PA ∩ B) = 0, then events A and B are

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

Events A and B are mutually exclusive if their joint probability is

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

If PA) = 0.45, PB) = 0.55, and PA ∪ B) = 0.78, then PA | B) =

If X and Y are independent events with PX) = 0.90 and PY) = 0.70, then PX∩Y) =

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Exam 4: Introduction to Probability

If two events are mutually exclusive, then their intersection

Two events, A and B, are mutually exclusive and each have a nonzero probability. If event A is known to occur, the probability of the occurrence of event B is

One of the basic requirements of probability is

Any process that generates well-defined outcomes is

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

Bayes' theorem is used to compute

If PA) = 0.7, PB) = 0.6, PA ∩ B) = 0, then events A and B are

The counting rule that is used for counting the number of experimental outcomes when n objects are selected from a set of N objects where order of selection is important is called

Events A and B are mutually exclusive if their joint probability is

If a penny is tossed three times and comes up heads all three times, the probability of heads on the fourth trial is

If PA) = 0.45, PB) = 0.55, and PA ∪ B) = 0.78, then PA | B) =

If X and Y are independent events with PX) = 0.90 and PY) = 0.70, then PX∩Y) =

Data and Statistics

Descriptive Statistics: Tabular and Graphical Displays

Descriptive Statistics: Numerical Measures

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Tests

Comparisons Involving Means, Experimental Design, and Analysis of Variance

Comparisons Involving Proportions and a Test of Independence

Simple Linear Regression

Multiple Regression

Filters