University of California at Berkeley
Department of Civil & Environmental Engineering
Structural Engineering Mechanics & Materials
Instructor:
Armen Der Kiureghian
Student name:__________________________
CE93  Engineering Data Analysis
Final Examination
Tuesday, May 17, 2005
Work on all four problems. Write clearly and state any assumptions you make. The exam
is closed books and notes, except for three sheets of paper and the table of Matlabfi dis
tributions.
The problems have the following weights:
Problem 1 (30 points) ________________________
Problem 2 (20 points) ________________________
Problem 3 (20 points) ________________________
Problem 4 (30 points) ________________________
Exam grade (100 points) ______________________
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Student name:__________________________________
2
Problem 1.
(10+10+10 = 30 points)
Timely completion of a construction project depends on the weather and on the working
conditions of machinery used on the job. The probabilities of delay for different combina
tions of weather condition (rain or no rain) and machinery breakdown are listed in the fol
lowing table:
Weather
Machinery
Probability of delay in completion of the project
No rain
No breakdown
0.05
Rain
No breakdown
0.20
No rain
Breakdown
0.30
Rain
Breakdown
0.60
Weather forecast indicates 30% chance of rain. From previous experience, we know that
the probability that the machinery will breakdown depends on the weather conditions
(due to the added force required to move wet soil). If it rains the probability of breakdown
is 0.25, whereas if it does not rain the probability of breakdown is only 0.10.
a)
Determine the probability that the construction job will be completed on time.
b) If the job is known to have been completed on time, what is the probability that it
rained?
c)
If the job is not completed on time, what is the probability that machinery breakdown
occurred?
Solution
Define R = rain, B = Breakdown, D = Delay.
a)
)
(
)

(
)
(
)

(
)
(
)

(
)
(
)

(
)
(
B
R
P
B
R
D
P
B
R
P
B
R
D
P
B
R
P
B
R
D
P
RB
P
RB
D
P
D
P
+
+
+
=
630
.
0
)
30
.
0
1
(
)
10
.
0
1
(
)
(
)

(
)
(
225
.
0
30
.
0
75
.
0
)
(
)

(
)
(
070
.
0
)
30
.
0
1
(
10
.
0
)
(
)

(
)
(
075
.
0
30
.
0
25
.
0
)
(
)

(
)
(
=
−
×
−
=
=
=
×
=
=
=
−
×
=
=
=
×
=
=
R
P
R
B
P
B
R
P
R
P
R
B
P
B
R
P
R
P
R
B
P
B
R
P
R
P
R
B
P
RB
P
143
.
0
630
.
0
05
.
0
225
.
0
20
.
0
070
.
0
30
.
0
075
.
0
60
.
0
)
(
=
×
+
×
+
×
+
×
=
D
P
857
.
0
143
.
0
1
)
(
1
=
−
=
−
D
P
Ans.
b)
)
(
)
(
)

(
)

(
R
P
D
P
R
D
P
D
R
P
=