chapter 1: probability theorysite.iugaza.edu.ps/ymadhoun/files/2016/09/lecture-01.pdf · 2017. 10....
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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: