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The first step is to
represent the problem by a decision tree. There are three key
symbols in a decision tree:
- A box represents
a decision node. Lines from the box denote the decision
alternatives (one line per decision alternative). The name of
the decision alternative goes above the line.
- A circle represents
a chance node. Lines from the circle denote the events
that could occur at the chance node. The name of the chance-driven
event goes above the line. The probability of the event goes
below the line. Since all probabilities at a chance node must
sum to 1.0, one event is labeled simply as #, to denote "1
- the sum of the probabilities of the other events."
- A horizontal rectangle
represents a terminal node. A terminal node represents
an outcome state, so there are no events that occur distal to
a terminal node. The value of the outcome appears in the rectangle.
A very simple decision
tree for medical versus surgical treatment might be that with
medication, the probability of life expectancy, (defined as the
average length of life remaining to a person) is .05. With surgery,
2 branches are possible - death and OK. The life expectancy for
the death arm is 0 and for the OK arm is
10
Question
2.3.1
What is
the probability represented for the OK arm?
 | The
sum of the life expectancies (LE) of each outcome at the chance
node, divided by the number of outcomes at that chance node
|
 | 1
plus the sum of the probabilities of the other events at the
chance node |
 | 1
minus the sum of the probabilities of the other events at
the chance node |
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