No facts about the future

• Uncertainty is present in every project.

• Risk management is the process, but probability and statistics provide the mathematical underpinning for the quantitative analysis of project risk.

Probability and projects

• The outcome of any single event, whether it is a coin toss or a project, cannot be known with certainty, but the pattern of behavior of a random event can be forecast.

• Single-point deterministic estimates forego the opportunity to estimate and forecast the impact of opportunity and threat.

• The relative frequency use of probability, such as "one chance in ten," forecasts a specific outcome; the subjective use of probability, such as "there is a 20% chance of rain today," expresses a "confidence" of an event within a range.

• Project events that are not mutually exclusive, or impose conditions that obviate independence between them, generally reduce the probability that either event will happen as planned.

• All probabilities of a single event must fall in the space of "zero to one" such that the equation p + (1-p) = 1 holds at all times.

Random variables

• If the outcome of a specific event has a numerical value, then the outcome is a variable, and because its value is not known with certainty before the fact, and could take on more than one value from event to event, it is a random variable.