Thinking Skills: Critical Thinking and Problem Solving

284 Unit 7 Critical reasoning: Advanced Level

Step 2

Now all that we have to do is insert the

likelihood of each of these outcomes in the

form of a percentage, and to multiply the

estimated value by its probability. (The

probability could be written as a number from

0 to 1, if preferred.) A triangle, or end node, is

placed at the end of each branch with the

product of the calculation beside it. These are

then added together to give the most likely

overall outcome of each decision.

To represent this mathematically we can

construct a tree diagram. We start with what is

known as a decision node, which by

convention is a rectangle, with the choices

branching out from it – hence the name ‘tree’.

At the same time we can write down the

known costs of each of these options next to

the respective branches.

Step 1

The next step is to add branches for each of

the possible outcomes. These branch out

from a second type of node, conventionally a

circle, called a chance node. We have data for

three levels of return, depending on the size

of the gas deposit, giving us three levels of

possible return, C, B and A. We can then do

the same for the three possible levels of

return that could come from an auction of

the extraction rights.

Step 3