How do unions and intersections describe events in probability theory?

In probability theory, unions and intersections are fundamental operations used to describe the relationships between events within a sample space.

• Intersection ($A\cap B$): This represents the set of all experimental outcomes that belong to both event $A$ and event $B$. It describes the occurrence of both events simultaneously.1
• Union ($A\cup B$): This represents the set of all experimental outcomes that belong to either event $A$, event $B$, or both. It describes the occurrence of at least one of the specified events.1

These operations are central to the principle of additivity. If events have no outcomes in common (meaning their intersection is the impossible event, denoted by $\varnothing$), the probability of their union is equal to the sum of their individual probabilities. This principle is a cornerstone of modern axiomatic probability.1

Would you like to explore how these concepts are visualized using Venn diagrams?