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CHAPTER FOUR
INTRODUCTION TO PROBABILITY
MULTIPLE CHOICE QUESTIONS
In the following multiple choice questions, circle the correct answer.
1.
Of five letters (A, B, C, D, and E), two letters are to be selected at random. How
many possible selections are there?
a. 20
b. 7
c. 5!
d. 10
e. 22
2.
Given that event E has a probability of 0.25, the probability of the complement of
event E
a. can not be determined with the above information
b. can have any value between zero and one
c. must be 0.75
d. is 0.25
e. None of the above answers is correct.
3.
Each individual outcome of an experiment is called
a. the sample space
b. a sample point
c. an experiment
d. an individual
e. None of the above answers is correct.
4.
The collection of all possible sample points in an experiment is
a. the sample space
b. a sample point
c. an experiment
d. the population
e. None of the above answers is correct.
5.
A graphical method of representing the sample points of an experiment is
a. a frequency polygon
b. a histogram
c. an ogive
d. a tree diagram
e. None of the above answers is correct.
6.
An experiment consists of selecting a student body president and vice president.
All undergraduate students (freshmen through seniors) are eligible for these
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offices. How many sample points (possible outcomes as to the classifications)
exist?
a. 4
b. 16
c. 8
d. 32
e. None of the above answers is correct.
7.
Three applications for admission to a local university are checked, and it is
determined whether each applicant is male or female. The number of sample
points in this experiment is
a. 2
b. 4
c. 6
d. 8
e. None of the above answers is correct.
8.
Assume your favorite football team has 2 games left to finish the season. The
outcome of each game can be win, lose or tie. The number of possible outcomes
is
a. 2
b. 4
c. 6
d. 8
e. None of the above answers is correct.
9.
Each customer entering a department store will either buy or not buy some
merchandise. An experiment consists of following 3 customers and determining
whether or not they purchase any merchandise. The number of sample points in
this experiment is
a. 2
b. 4
c. 6
d. 8
e. None of the above answers is correct.
10.
An experiment consists of tossing 4 coins successively. The number of sample
points in this experiment is
a. 16
b. 8
c. 4
d. 2
e. None of the above answers is correct.
11.
Any process that generates well-defined outcomes is
a. an event
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b.
c.
d.
e.
an experiment
a sample point
all of the above answers are correct
None of the above answers is correct.
12.
The sample space refers to
a. any particular experimental outcome
b. the sample size minus one
c. the set of all possible experimental outcomes
d. both a and c are correct
e. None of the above answers is correct.
13.
In statistical experiments, each time the experiment is repeated
a. the same outcome must occur
b. the same outcome can not occur again
c. a different outcome may occur
d. None of the above answers is correct.
14.
When the assumption of equally likely outcomes is used to assign probability
values, the method used to assign probabilities is referred to as the
a. relative frequency method
b. subjective method
c. probability method
d. classical method
e. None of the above answers is correct.
15.
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 answers is correct.
16.
A method of assigning probabilities based upon judgment is referred to as the
a. relative method
b. probability method
c. classical method
d. frequency method
e. None of the above answers is correct.
17.
A sample point refers to the
a. numerical measure of the likelihood of the occurrence of an event
b. set of all possible experimental outcomes
c. individual outcome of an experiment
d. All of the above answers are correct.
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e. None of the above answers is correct.
18.
A graphical device used for enumerating sample points in a multiple-step
experiment is a
a. bar chart
b. pie chart
c. histogram
d. cumulative frequency distribution
e. None of the above answers is correct.
19.
An experiment consists of three steps. There are four possible results on the first
step, three possible results on the second step, and two possible results on the
third step. The total number of experimental outcomes is
a. 9
b. 14
c. 24
d. 36
e. None of the above answers is correct.
20.
Since the sun must rise tomorrow, then the probability of the sun rising tomorrow
is
a. much larger than one
b. zero
c. infinity
d. any value over 100
e. None of the above answers is correct.
21.
If two events are independent, then
a. they must be mutually exclusive
b. the sum of their probabilities must be equal to one
c. their intersection must be zero
d. All of the above answers are correct.
e. None of the above answers is correct.
22.
Bayes theorem is used to compute
a. the prior probabilities
b. the union of events
c. both a and b
d. the posterior probabilities
e. None of the above answers is correct.
23.
The intersection of two mutually exclusive events
a. can be any value between 0 to 1
b. must always be equal to 1
c. must always be equal to 0
d. can be any positive value
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e. None of the above answers is correct.
24.
Two events are mutually exclusive
a. if their intersection is 1
b. if they have no sample points in common
c. if their intersection is 0.5
d. both a and c are correct
e. None of the above answers is correct.
25.
The range of probability is
a. any value larger than zero
b. any value between minus infinity to plus infinity
c. zero to one
d. any value between -1 to 1
e. None of the above answers is correct.
26.
Which of the following statements is(are) always true?
a. -1  P(Ei) 1
b. P(A) = 1 - P(Ac)
c. P(A) + P(B) = 1
d. both b and c
e. None of the above answers is correct.
27.
Events that have no sample points in common are
a. independent events
b. posterior events
c. mutually exclusive events
d. complements
e. None of the above answers is correct.
28.
Initial estimates of the probabilities of events are known as
a. sets
b. posterior probabilities
c. conditional probabilities
d. prior probabilities
e. None of the above answers is correct.
29.
Two events with nonzero probabilities
a. can be both mutually exclusive and independent
b. can not be both mutually exclusive and independent
c. are always mutually exclusive
d. both b and c
e. None of the above answers is correct.
30.
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
5
a.
b.
c.
d.
e.
one
any positive value
zero
any value between 0 to 1
None of the above answers is correct.
31.
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. None of the above answers is correct.
32.
On a December day, the probability of snow is .30. The probability of a "cold"
day is .50. The probability of snow and "cold" weather is .15. Are snow and
"cold" weather independent events?
a. only if given that it snowed
b. no
c. yes
d. only when they are also mutually exclusive
e. None of the above answers is correct.
33.
One of the basic requirements of probability is
a. for each experimental outcome Ei, we must have P(Ei)  1
b. P(A) = P(Ac) - 1
c. if there are k experimental outcomes, then P(Ei) = 1
d. both b and c
e. None of the above answers is correct.
34.
The symbol  shows the
a. union of events
b. intersection of two events
c. sum of the probabilities of events
d. sample space
e. None of the above answers is correct.
35.
The symbol  shows the
a. union of events
b. intersection of two events
c. sum of the probabilities of events
d. sample space
e. None of the above answers is correct.
36.
The multiplication law is potentially helpful when we are interested in computing
the probability of
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a.
b.
c.
d.
e.
mutually exclusive events
the intersection of two events
the union of two events
conditional events
None of the above answers is correct.
37.
If two events are mutually exclusive, then their intersection
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
e. None of the above answers is correct.
38.
The union of events A and B is the event containing
a. all the sample points belonging to B or A
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 answers is correct.
39.
If a penny is tossed four times and comes up heads all four times, the probability
of heads on the fifth trial is
a. zero
b. 1/32
c. 0.5
d. larger than the probability of tails
e. None of the above answers is correct.
40.
If a coin is tossed three times, the likelihood of obtaining three heads in a row is
a. zero
b. 0.500
c. 0.875
d. 0.125
e. None of the above answers is correct.
41.
The union of two events with nonzero probabilities
a. can not be less than one
b. can not be one
c. both a and b are correct
d. could be larger than one
e. None of the above answers is correct.
42.
If P(A) = 0.5 and P(B) = 0.5, then P(A  B)
a. is 0.00
b. is 0.25
c. is 1.00
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d. is 0.5
e. can not be determined from the information given
43.
If A and B are independent events with P(A) = 0.4 and P(B) = 0.6, then
P(A  B) =
a. 0.76
b. 1.00
c. 0.24
d. 0.2
e. None of the above answers is correct.
44.
If A and B are independent events with P(A) = 0.2 and P(B) = 0.6, then
P(A  B) =
a. 0.62
b. 0.12
c. 0.60
d. 0.68
e. None of the above answers is correct.
45.
If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then
P(AB) =
a. 0.05
b. 0.0325
c. 0.65
d. 0.8
e. None of the above answers is correct.
46.
If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then
P(A  B) =
a. 0.30
b. 0.15
c. 0.00
d. 0.20
e. None of the above answers is correct.
47.
If A and B are mutually exclusive events with P(A) = 0.3 and P(B) = 0.5, then
P(A  B) =
a. 0.00
b. 0.15
c. 0.8
d. 0.2
e. None of the above answers is correct.
48.
A lottery is conducted using three urns. Each urn contains chips numbered from 0
to 9. One chip is selected at random from each urn. The total number of sample
points in the sample space is
8
a.
b.
c.
d.
e.
30
100
729
1,000
None of the above answers is correct.
49.
Of the last 100 customers entering a computer shop, 25 have purchased a
computer. If the classical method for computing probability is used, the
probability that the next customer will purchase a computer is
a. 0.25
b. 0.50
c. 1.00
d. 0.75
e. None of the above answers is correct.
50.
Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. The
complement of Event B equals
a. 0.00
b. 0.06
c. 0.7
d. 0.1
e. None of the above answers is correct.
51.
An experiment consists of four outcomes with P(E1) = 0.2, P(E2) = 0.3, and
P(E3) = 0.4. The probability of outcome E4 is
a. 0.500
b. 0.024
c. 0.100
d. 0.900
e. None of the above answers is correct.
52.
Events A and B are mutually exclusive. Which of the following statements is also
true?
a. A and B are also independent.
b. P(A  B) = P(A)P(B)
c. P(A  B) = P(A) + P(B)
d. P(A  B) = P(A) + P(B)
e. None of the above answers is correct.
53.
A six-sided die is tossed 3 times. The probability of observing three ones in a row
is
a. 1/3
b. 1/6
c. 1/27
d. 1/216
e. None of the above answers is correct.
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54.
The probability of the occurrence of event A in an experiment is 1/3. If the
experiment is performed 2 times and event A did not occur, then on the third trial
event A
a. must occur
b. may occur
c. could not occur
d. has a 2/3 probability of occurring
e. None of the above answers is correct.
55.
A perfectly balanced coin is tossed 6 times and tails appears on all six tosses.
Then, on the seventh trial
a. tails can not appear
b. heads has a much larger chance of appearing than tails
c. tails has a better chance of appearing than heads
d. heads must appear
e. None of the above answers is correct.
56.
In an experiment, events A and B are mutually exclusive. If P(A) = 0.6, then the
probability of B
a. can not be larger than 0.4
b. can be any value greater than 0.6
c. can be any value between 0 to 1
d. can not be determined with the information given
e. None of the above answers is correct.
57.
The set of all possible sample points (experimental outcomes) is called
a. a sample
b. an event
c. the sample space
d. a population
e. None of the above answers is correct.
58.
A method of assigning probabilities which assumes that the experimental
outcomes are equally likely is referred to as the
a. objective method
b. classical method
c. subjective method
d. experimental method
e. None of the above answers is correct.
59.
A method of assigning probabilities based on historical data is called the
a. classical method
b. subjective method
c. relative frequency method
d. None of the above answers is correct.
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60.
The probability assigned to each experimental outcome must be
a. any value larger than zero
b. smaller than zero
c. one
d. at least one
e. between zero and one
61.
If P(A) = 0.38, P(B) = 0.83, and P(A  B) = 0.57; then P(A  B) =
a. 1.21
b. 0.64
c. 0.78
d. 1.78
e. None of the above answers is correct.
62.
If P(A) = 0.50, P(B) = 0.60, and P(A  B) = 0.30; then events A and B are
a. mutually exclusive events
b. not independent events
c. independent events
d. not enough information is given to answer this question
e. None of the above answers is correct.
63.
If P(A) = 0.62, P(B) = 0.47, and P(A  B) = 0.88; then P(A  B) =
a. 0.2914
b. 1.9700
c. 0.6700
d. 0.2100
e. None of the above answers is correct.
64.
If P(A) = 0.85, P(A  B) = 0.72, and P(A  B) = 0.66, then P(B) =
a. 0.15
b. 0.53
c. 0.28
d. 0.15
e. None of the above answers is correct.
65.
If A and B are independent events with P(A) = 0.4 and P(B) = 0.25, then
P(A  B) =
a.
b.
c.
d.
e.
66.
0.65
0.55
0.10
Not enough information is given to answer this question.
None of the above answers is correct.
If a penny is tossed three times and comes up heads all three times, the probability
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of heads on the fourth trial is
a. smaller than the probability of tails
b. larger than the probability of tails
c. 1/16
d. 0.0625
e. None of the above answers is correct.
67.
If P(A) = 0.80, P(B) = 0.65, then, and P(A  B) = 0.78, then P(BA) =
a. 0.6700
b. 0.8375
c. 0.9750
d. Not enough information is given to answer this question.
e. None of the above answers is correct.
68.
If A and B are independent events with P(A) = 0.38 and P(B) = 0.55, then
P(AB) =
a. 0.209
b. 0.000
c. 0.550
d. Not enough information is given to answer this question.
e. None of the above answers is correct.
69.
If X and Y are mutually exclusive events with P(X) = 0.295, P(Y) = 0.32, then
P(XY) =
a. 0.0944
b. 0.6150
c. 1.0000
d. 0.0000
e. None of the above answers is correct
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