Editing Probability space (section)

=== Mutual exclusivity ===
{{Main article|Mutual exclusivity}}
Two events, {{math|''A''}} and {{math|''B''}} are said to be mutually exclusive or ''disjoint'' if the occurrence of one implies the non-occurrence of the other, i.e., their intersection is empty. This is a stronger condition than the probability of their intersection being zero.

If {{math|''A''}} and {{math|''B''}} are disjoint events, then {{math|1=''P''(''A'' ∪ ''B'') = ''P''(''A'') + ''P''(''B'')}}. This extends to a (finite or countably infinite) sequence of events. However, the probability of the union of an uncountable set of events is not the sum of their probabilities. For example, if {{mvar|Z}} is a [[normal distribution|normally distributed]] random variable, then {{math|1=''P''(''Z'' = ''x'')}} is 0 for any {{mvar|x}}, but {{math|1=''P''(''Z'' ∈ '''R''') = 1}}.

The event {{math|''A'' ∩ ''B''}} is referred to as "''A'' and ''B''", and the event {{math|''A'' ∪ ''B''}} as "''A'' or ''B''".