Mathematics for Maintenance: Basic Concepts and Tools

Abstract

The probability P(E) of an event is a number lying between 0 and 1 that measures, in some sense, the likelihood of the event occurring. It can be derived either by enumerating all the possibilities:

$$ P(E) = \frac{{number\;of\;cases\;favourable\;to\;E}}{{total\;number\;of\;possoible\;cases}} $$

which gives the ‘true’ probability (the difficulty is to carry out the enumeration) — or by an experimental procedure based on observations: if a number n of observations are made, in each of which E might occur, and if f _n (E) is the fraction in which E is observed to occur, then:

$$ P(E) = \lim \int_n {(E)\quad as\quad n \to \infty } $$

This is the ‘frequency’ definition of probability; the greater the number of observations, the closer the frequency approaches, the ‘true’ probability.