What Are Disjoint Events in Probability?

$Colorful House of Math logo$

Numbers and Quantities

Algebra

Geometry

Statistics and Probability

Functions

Proofs

Encyclopedia>Statistics and Probability>Probability and Combinatorics>Basic Probability>What Are Disjoint Events in Probability?

Video Crash Courses

Want to watch animated videos and solve interactive exercises about disjoint events?

Click here to try Video Crash Courses called “Single Trial”!

Theory

Disjoint Events

Disjoint events are events that never occur together. Two events $A$ and $B$ are disjoint if the intersection of the sets is empty. Mathematically, this is written as

\begin{array}{l} P (A \cap B) & = 0 \\ because A \cap B & = no elements. \end{array}

P (A \cap B) = 0 because A \cap B = no elements.

Disjoint events

Example 1

You roll a die. Let $A$ be the compound event defined as “more than four dots”, $A = {5, 6}$ , and $B$ be “fewer than three dots”, $B = {1, 2}$ . That means the intersection between $A$ and $B$ is the empty set, because they have no outcomes in common. They can never both occur at once.

You denote the empty set with the symbol $\emptyset$ .

Note! Complementary outcomes are always disjoint, because an event can not both happen and not happen at the same time.

Want to know more?Sign UpIt's free!

What Is Union and Intersection of Sets?

Want to know more?Sign UpIt's free!

What Are Complementary Events in Probability?