# pairwise disjoint events example

Can someone please give me an example of a pairwise disjoint event?

Let $S = \{1,2,3,4,5,6,7,8,9\}.$

Will pairwise disjoint events be: $\{1\},\{2\},\{3,4\},\{5,6,7,8,9\}$?

In order to be pairwise disjoint event does it just mean that for all $A_i$ inside $S$ the intersection between $A_i$ and $A_j$ ($j$ not equal $i$) is the empty set?

• Note that "a pairwise disjoint event" is an odd concept. Rather, one should find "pairwise disjoint events". – Did Aug 1 '13 at 13:53

It's worth noting that pairwise disjoint events needn't cover all outcomes (as they do in your example). For example, the events $\{1\},$ $\{2\},$ $\{3,4\},$ $\{5,6\}$ are also pairwise disjoint, but $7,8,9$ are not outcomes present in these events. Your example is what is known as a partition of the sample space.