Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 1

Chapter 1: Probability Theory

Section 1.1: Probabilities

Problem (01): 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 (02): 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:

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 2

Problem (03): 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 (04): 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:

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 3

Problem (05): 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:

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 4

Section 1.2: Events

Problem (01):

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:

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 5

Problem (02): 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 (03): 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:

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 6

Problem (04): 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 (05): 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 probabilities

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 7

of the six outcomes are given in the figure below. What is the probability

that:

(1) the type I battery lasts longest?

(2) the type I battery lasts shortest?

(3) the type I battery does not last longest?

(4) the type I battery lasts longer than the type II battery?

(Problem 1.2.10 in textbook)

Solution:

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 8

Problem (06): 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) both assembly lines are shut down?

(2) neither assembly line is shut down?

(3) at least one assembly line is at full capacity?

(4) exactly one assembly line is at full capacity?

(5) 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:

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 9

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 10

Problem (07): 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:

Civil Engineering Department: Engineering Statistics (ECIV 2005)

Engr. Yasser M. Almadhoun Page 11

Problem (08) 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: