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CE 398 Introduction to Civil Engineering Systems Design, Fall 2011
Homework 3 (Basics of Probability for CE Systems Development)
Due: Thursday September 15
Name: SOLUTIONS
Q.1
Consider two events
P
and
Q
.
a)
Write the general formula used to calculate the probability that either event
P
occurs or
Q
occurs or both
occur.
p
(P U Q) =
p
(P) +
p
(Q) –
p
(P ∩ Q)
b) How does this formula change if …
(i) Events
P
and
Q
are disjoint (that is, mutually exclusive of each other)
(Give an example of such pair of events in everyday life or civil engineering)
p
(P U Q) =
p
(P) +
p
(Q)
Example:
Joe gets a final grade of A in CE398
Joe gets a final grade of B in CE 398
(ii Events
P
and
Q
are nondisjoint events that are statistically independent of each other.
(Give an example of such pair of events in everyday life or civil engineering)
p
(P U Q) =
p
(P) +
p
(Q) –
p
(P)*
p
(Q)
There is a recent serious earthquake in Lafayette
This year’s winter is unusually severe
(iii) Events
P
and
Q
are nondisjoint events that are statistically dependent of each other.
(Give an example of such pair of events in everyday life or civil engineering)
p
(P U Q) =
p
(P) +
p
(Q) –
p
(P)*
p
(Q/P)
or
p
(P U Q) =
p
(P) +
p
(Q) –
p
(Q)*
p
(P/Q)
There is a serious earthquake in Lafayette
Bridge systems in Lafayette suffer some deterioration
1
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View Full Document Q.2.
The probability that Joe is late for work is 0.20. The probability that Joe drives fast to work is 0.40.
The probability that Joe does a good job at work is 0.75.
Choose 3 letters, say L, D, G, to denote each of these events.
If Joe is late, he the probability that he drives fast to work is 0.9. Also, assume that his punctuality (or
otherwise) to work does not influence whether he does a good job that day. Furthermore, 30 out of every
100 days, he drives fast to work and does a good job in the same day.
(a) For all paired combinations of these two events, comment on their mutual exclusivity, statistical
dependence, or statistical independence. Use the table below.
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This note was uploaded on 01/20/2012 for the course CIVIL ENGI 398 taught by Professor Labi during the Spring '11 term at Purdue UniversityWest Lafayette.
 Spring '11
 LABI

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