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Q
uantitative
R
easoning &
P
roblem
S
olving
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© 2014 Pacific Crest
O
ops
! A
voiding
C
ommon
E
rrors
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Assuming that an event was random when intentional
Example
: The theme of making a murder appear to be accidental is a popular one in movies. In
the film Double Indemnity, the murder was made to look random even though it had
been planned for the purpose of collecting life insurance money.
Why?
If an insurance company doesn’t believe that something is an act of God, but a
deliberate act/decision, they won’t want to pay out. The company doesn’t have the
resources to check every single claim. They have to determine when something
doesn’t really seem random. When insurance companies pay off, they want to make
sure that the specific occurrence is actually random.
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Assuming that an event was intentional when it was random
Example: A student shows up late for class for the fourth time and, following course policy, the
instructor penalized the student by 10 points on the next exam. The student tries to
explain that he was tardy because he was carjacked.
Why:
The course policy made no distinction between random/uncontrollable circumstances
and circumstances that could/should have been controlled. Most people would agree
that a carjacking is random event and that the student had no control over it happening
to him. Once the student explained, his instructor relented but asked the student about
the three previous tardies and how much of each was potentially within the student’s
control. The student had to admit that oversleeping, poor planning, and running
out of gas (the reasons for the previous tardies) were within his control, unlike the
carjacking, and could have been avoided.
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There is a winning strategy in gambling
Example:
One popular strategy is doubling your bet when you lose. The belief is that you can
always recoup your loses by doubling until you win.
Why:
There is always a chance that a run of losses while doubling the bet can exceed your
total capital for betting. It will never exceed the house’s capital because it is infinite
(the house has the authority to cut you off).
A
re You Ready?
Before continuing, you should be able to ...
I can...
OR
Here’s my question...
think through a situation and find the
random components
rank the random components based on
their significance
predict why some events are more likely
than other events