Sets are central in probability theory. When considering probabilities within the context of set theory, it will be easier to structure exercises.
“ union ” is all the elements in , or both. Mathematically, this is written as follows:
You read as “or”.
In other words, is a new compound set consisting of all the outcomes unique to , all outcomes unique to , as well as all the outcomes that and have in common. You can visualize it with this Venn diagram:
Let be the set and be the set . The union is the set of outcomes .
The “intersection of and ” is all the elements that are in both and , and can be written:
You read as “and”.
In other words, is composed of the outcomes that are in both and . It’s visualized with this Venn diagram:
The intersection in the Venn diagram represents the overlap between and .
You roll a die. Let be the event “even number of dots”, which is the set , and be the event “more than three dots”, which is the set . That means the intersection is the set .