An event A is something which either occurs or does not occur in a particular case. It often has some kind of verbal description: e.g. ‘I win the game’ or ‘the patient survives’. As we saw in Section 2.3, the formal characterization of the event is as a set of realizations ω, i.e. a subset of Ω, also denoted by A. This is just the set of realizations for which the event occurs. The probability of the event is defined as P(A) = E[I(A)], (1) where I(A, ω) is the indicator function of the set A; the random variable which takes value 1 or 0 according as the event occurs or not. Thus P(A) can be seen as the expected proportion of times that A occurs.
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