In probability theory, we usually see that it is stated that events are pairwise disjoint rather than simply disjoint events.
The word “pairwise” in “pairwise disjoint” is superfluous: a collection of sets is disjoint if no element appears in more than one of the sets at a time. It means that every pair of distinct sets in the collection has an empty intersection. However, including the “pairwise” emphasizes that the property can be checked at the level of pairs from the collection.
For example, suppose we have a collection of few events with the followings values: {1,2}, {2,3}, {3,4}, {4,5}, {5,6} and if we take intersection then we will get empty set.
{1,2} 
{2,3} {3,4} {4,5} {5,6} = 
.
However, if we take pairwise intersection then will get a common element in every pair. Like intersection of {1,2} {2,3} = {2}.
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“Difference between pairwise disjoint and disjoint in probability theory” From NotePub.io – Publish & Share Note! https://notepub.io/questions/what-is-the-difference-between-pairwise-disjoint-and-disjoint-in-probability-theory/
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