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ESI 6321
APPLIED PROBABILITY METHODS IN ENGINEERING
OEM 2009
February 16, 2008
MIDTERM+SOLUTIONS
8:0010:00AM
Open book, open lecture notes
This test consists of 3 problems
Name:
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Problem 1: (35 points)
A nuclear power company is deciding whether to build a nuclear power plant at Diablo
Canyon or at Roy Rogers City. The cost of building the power plant is $10 million at
Diablo Canyon and $20 million at Roy Rogers City. If the company builds at Diablo
Canyon, however, and an earthquake occurs at Diablo Canyon during the next five years,
construction will be terminated and the company will lose $10 million (and will still have
to build a power plant at Roy Rogers City).
A priori, the company believes there is a 20% chance that an earthquake will occur at
Diablo Canyon during the next five years. For $1 million, a geologist can be hired to
analyze the fault structure at Diablo Canyon. He will either predict that an earthquake
will occur or that an earthquake will not occur. The geologist’s past record indicates that
he will predict an earthquake on 95% of the occasions for which an earthquake will
indeed occur, and no earthquake on 90% of the occasions for which an earthquake will
not occur.
Assume that the company’s goal is to minimize its total expected cost.
(a)
Should the power company hire the geologist?
Solution:
Let E denote the event that an earthquake will occur in the next five years.
Let G denote the event that the geologist predicts that an earthquake will occur in the
next five years.
We are given the following probabilities:
P(E) = 0.20
P(GE) = 0.95
P(G’E’) = 0.90
For the decision tree, we require the following probabilities:
P(G) = P(GE) P(E) + P(GE’) P(E’) = 0.95
×
0.20 + (10.90)
(10.20) = 0.27
P(EG) = P(GE) P(E) / P(G) = 0.95
0.20 / 0.27 = 0.704
P(EG’) = P(G’E) P(E) / P(G’) = (10.95)
0.20 / (10.27) = 0.0137
The company should hire a geologist, for a total expected cost of $13.9 million.
(b)
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 Spring '07
 JosephGeunes

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