our intuitive definition of probability as a fraction of occurrence.
The second axiom states that the event described by the entire sample space has probability of 1. If ω is the
outcome of an experimental trial, then ω ∈ Ω, by the definition of the sample space, so the event described
by Ω must occur on every trial. Intuitively, we can say that every experiment we perform must yield some
kind of result, and that result must be in the sample space, so the “event” described by the sample space is
so general that it must always occur.
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The third axiom describes how to combine the probabilities of mutually exclusive (also called disjoint) events.
Intuitively, if E and F cannot occur at the same time, then the fraction of time that E or F occurs is the
sum of the fractions of time that E and F occur individually.