10. a. According to the decision tree, the agency should not take the case to
court:
b. According to the joint table, Pr(P|Q) = .15/.31 = .484 and
Pr(P|C) = .05/.69 = .07.
Audit Result Padding Not
c. According to the accompanying decision tree, the agency should
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No
0
-.2
-$.5
.8
-$.
5
.25
No
c. As the accompanying decision tree shows, your company’s expected
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b. Multiple risks made it more difficult to detect the increased risk. Overall,
Ford SUVs did not have elevated rollover rates. Overall, Firestone tires
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8$40
.8
c. Both were undeniably contributing factors. Ford argued that its vehicle
and recommended tire pressure and loadings were not at fault. Similar
size tires (from other manufacturers and even Firestone itself) under
For more information on this subject see:
“Answers still Elusive in Tire Crisis,” The New York Times, September 15,
2000, p. B1.
“Documents Portray Tire Debacle as a Story of Lost Opportunities,” The
“How Firestone Let the Warnings Slide by as Debacle Developed,” The Wall
“How the Tire Problem Turned into a Crisis for Firestone and Ford,” The
Spreadsheet Problem
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S1. a. Cell E20 has the value .045, and Cell F20 has the value .003. For
instance, we compute Pr(average & 15 of 20) as: Pr(average)*Pr(15 of
b. The last probability shows that this good a performance record is very
unlikely (except by pure luck) to have come from an inferior
fore-caster. Still, it’s over 50 percent likely that the manager is
c. Superior performers have only a 4 percent advantage over average
Bonus Problem
An oil wildcatter is considering drilling a site that she judges to be wet
with probability .2 and dry with probability .8. Her profit from an oil strike
is $1 million, and her loss from a dry hole is -$800,000.
a. Before drilling, the wildcatter can pay for a seismic test that will return
b. For a comparable fee, the wildcatter can find out whether a recently
drilled well nearby struck oil (O) or not (N). If the wildcatter’s site were
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Answer
a. For the seismic test, the revised probabilities are: Pr(W|G) = .15/.35 = 3/7,
b. If the wildcatter learns the results of the nearby site, the revised
probabilities are Pr(W|O) = .2/.4 = .5, and Pr(W|N) = 0/.6 = 0. If the
c. The accompanying table shows the joint probabilities if both sources of
information are available. Note that there are four possible observations.
Site is:
Wet Dry Total
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