We can apply certain aspects of set theory to our study of probabilities with the hel of complements, unions and intersections. This becomes useful when we want to combine the probabilities of distinct events. In this article, we will discuss how to formally articulate the intersection of events; a process that involves combining concepts in probability theory and set theory.

For example, we can talk about the possibility of something being both a spade and a face card:

E1 = { x | x is a spade}

E2 = {x | x is a face card}

We would use the set theory function of intersection to formally talk about the probability that a card will be both a face card and a spade in the following way:

E3 = { x | x is in E1 and x is in E2 } = E1 ∩ E2

More simply, we can speak of this in the following way:

P (E1 ∩ E2).

We further define this in the following way:

P(E1 ∩ E2) = |E1 ∩ E2| / |S|

Steinhart, Eric. “More Precisely: The Mathematics You Need To Do Philosophy.” Broadview Press, 2009.