The (1-p) Space

To this point, we have been using a number of conventions adopted for probability analysis:

• All quantitative probabilities lie in the range between the numbers 0 (absolute certainty that an outcome will not occur) and 1 (absolute certainty that an outcome will occur).

• The lower case "p" is the notation for probability; it stands for a number between 0 and 1 inclusively. Typically, "p" is expressed as a decimal.

• If "p" is the probability that project outcome A will happen, then "1-p" is the probability that project outcome A will not occur. We then have the following equation: p + (1-p) = 1 at all times. More rigorously, we write: p(A) + [1-p(A)] = 1, where the notation p(A) means "probability that A will occur."

• "1-p" is the probability that something else, say project outcome B, will happen instead of A. After all, there cannot be a vacuum in the project for lack of outcome A. Sometimes outcome B is most vexing for project managers. B could well be a "known unknown." To wit: Known...A may not happen, but then unknown...what will happen, what is B?

• Sometimes it is said: B is in the (1-p) space of A, or the project manager might ask his or her team: "What is in the (1-p) space of A?"

• Project managers must always account for all the scope and be aware of all the outcomes. Thus: p(A) + p(B) = 1. A common mistake made by the project team is to not define or identify B, focusing exclusively on A.

Of course, there may be more possibilities than just B in the (1-p) space of A. Instead of just B, there might be B, C, D, E, and so forth. In that case, the project manager or risk analyst must be very careful to obey the following equation:

[1-p(A)] = p(B) + p(C) + p(D) + p(E) + ...

The error that often occurs is that the right side sums up too large. That is, we have the condition:

p(A) + p(1-A) > 1

On the right side, there are either too many possibilities identified, their respective probabilities are too large, or on the left side, the probabilities of A are misjudged. It is left to the project team to recognize the error of the situation and take corrective measures.