Civil Engineering Department: Engineering Statistics (ECIV 2005)
Chapter 1: Probability Theory
Section 1.1: Probabilities
Problem (1):
A car repair is performed either on time or late and either satisfactorily or
unsatisfactorily. What is the sample space for a car repair?
(problem 1.1.5 in textbook)
Solution:
Problem (2):
A bag contains balls that are either red or blue and either dull or shiny.
What is the sample space when a ball is chosen from the bag?
(problem 1.1.6 in textbook)
Solution:
Engr. Yasser M. Almadhoun
Page 1
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Problem (3):
An experiment has five outcomes, I, II, III, IV, and V. If: P(I) = 0.08,
P(II) = 0.20, and P(III) = 0.33, what are the possible values for the
probability of outcome V? If outcomes IV and V are equally likely, what
are their probability values?
(problem 1.1.9 in textbook)
Solution:
Problem (4):
An experiment has three outcomes, I, II, and III. If outcome I is twice as
likely as outcome II, and outcome II is three times as likely as outcome
III, what are the probability values of the three outcomes?
(problem 1.1.10 in textbook)
Solution:
Engr. Yasser M. Almadhoun
Page 2
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Problem (5):
A company`s advertising expenditure is either low with probability 0.28,
average with probability 0.55, or high with probability p. What is p?
(problem 1.1.11 in textbook)
Solution:
Engr. Yasser M. Almadhoun
Page 3
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Section 1.2: Events
Problem (1):
Consider the sample space in the figure below with outcomes a, b, c, d, e,
and f. If P(A) = 0.27, calculate:
1. P(b)
2. P(A`)
3. P(d)
(problem 1.2.2 in textbook)
Solution:
Engr. Yasser M. Almadhoun
Page 4
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Problem (2):
If birthdays are equally likely to fall on any day, what is the probability
that a person chosen at random has a birthday in January? What about
February?
(problem 1.2.3 in textbook)
Solution:
Problem (3):
When a company introduces initiatives to reduce its carbon footprint, its
costs will either increase, stay the same, or decrease. Suppose that the
probability that the costs increase is 0.03, and the probability that the
costs stay the same is 0.18. What is the probability that costs will
decrease? What is the probability that costs will not increase?
(problem 1.2.4 in textbook)
Solution:
Engr. Yasser M. Almadhoun
Page 5
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Problem (4):
Two fair dice are thrown, one red and one blue. What is the probability
that the red die has a score that is strictly greater than the score of the blue
die? Why is this probability less than 0.5? What is the complement of this
event?
(problem 1.2.6 in textbook)
Solution:
Problem (5):
Three types of batteries are being tested, type I, type II, and type III. The
outcome (I, II, III) denotes that the battery of type I fails first, the battery
of type II next, and the battery of type III lasts the longest. The
Engr. Yasser M. Almadhoun
Page 6
Civil Engineering Department: Engineering Statistics (ECIV 2005)
probabilities of the six outcomes are given in the figure below. What is
the probability that:
1.
2.
3.
4.
the type I battery lasts longest?
the type I battery lasts shortest?
the type I battery does not last longest?
the type I battery lasts longer than the type II battery?
(problem 1.2.10 in textbook)
Solution:
Engr. Yasser M. Almadhoun
Page 7
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Problem (6):
A factory has two assembly lines, each of which is shutdown (S), at
partial capacity (P), or at full capacity (F). The sample space is given in
the figure below, where, for example, (S, P) denotes that the first
assembly line is shut down and the second one is operating at partial
capacity.
(A) What is the probability that:
1.
2.
3.
4.
5.
both assembly lines are shut down?
neither assembly line is shut down?
at least one assembly line is at full capacity?
exactly one assembly line is at full capacity?
no more than one assembly line is at full capacity?
(B) What is the complement of the event in part (2) and its probability?
What is the complement of the event in part (3) and its probability?
(problem 1.2.11 in textbook)
Solution:
Engr. Yasser M. Almadhoun
Page 8
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Engr. Yasser M. Almadhoun
Page 9
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Problem (7):
A company`s revenue is considerably below expectation with probability
0.08, is slightly below expectation with probability 0.19, exactly meets
expectation with probability 0.26, is slightly above expectation with
probability 0.36, and is considerably above expectation with probability
0.11. What is the probability that the company`s revenue is not below
expectation?
(problem 1.2.13 in textbook)
Solution:
Problem (8)
An advertising campaign is cancelled before launch with probability 0.10,
is launched but cancelled early with probability 0.18, is launched and
runs its targeted length with probability 0.43, and is launched and is
extended beyond its targeted length with probability 0.29. What is the
probability that the advertising campaign is launched?
(problem 1.2.14 in textbook)
Solution:
Engr. Yasser M. Almadhoun
Page 10
Civil Engineering Department: Engineering Statistics (ECIV 2005)
Engr. Yasser M. Almadhoun
Page 11