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

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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.

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What Is Union and Intersection of Sets?

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What Are Complementary Events in Probability?

What Are Disjoint Events in Probability?

Statistics

Probability and Combinatorics

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