pairwise disjoint events example

Question

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 01 '13 at 13:53

score 8 · Accepted Answer · answered Aug 01 '13 at 13:51

That is precisely what it means. Your example works just fine.

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.

pairwise disjoint events example

1 Answers1