Statistics for Maintenance Modelling: Basic Probability Concepts

# Propositions of Probability¤

## Proposition 1:

P(E) = 1 - P(E)

This states that the probability that an event does not occur is 1 minus the probability that the event does occur.

This proposition is derived from the fact that EE = S.

## Proposition 2:

If EF, then P(E) P(F)

If event E is contained in event F, then the probability of E is no greater than the probability of event F.

## Proposition 3:

P(EF) = P(E) + P(F) - P(EF)

This states that the probability of event E or F or both occurring is the sum of their respective probabilities minus the probability of E and F occuring.

This proposition can be proved using a Venn diagram where (EF) is divided into three mutually exclusive sections. Click here for the proof.

Click here for an example.