Statistics for Maintenance Modelling: Basic Probability Concepts

# Proof of Proposition 2¤

That P(E) P(F) if EF can be proved as follows:

Since EF, it follows that we can express F as:

F = EEF

Since E and F are mutually exclusive, we obtain from axiom 3 that:

For any sequence of mutually exclusive events E1, E2 etc., the probability of at least one of these mutually exclusive events occurring is just the sum of their respective probabilities.

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

which proves the result since P(EF) 0

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