# Definition:Event/Occurrence/Union

(Redirected from Definition:Union of Events)

## Definition

Let the probability space of an experiment $\EE$ be $\struct {\Omega, \Sigma, \Pr}$.

Let $A, B \in \Sigma$ be events, so that $A \subseteq \Omega$ and $B \subseteq \Omega$.

Let the outcome of the experiment be $\omega \in \Omega$.

Let $\omega \in A \cup B$, where $A \cup B$ denotes the union of $A$ and $B$.

Then either $A$ or $B$ occur.

## Examples

### Both Prime and Even

Consider the experiment $\EE$ such that $2$ (positive) integers are drawn at random from a table of random numbers.

Let $A$ be the event that at least $1$ of these integers is prime.

Let $B$ be the event that at least $1$ of these integers is even.

Then their union $A \cup B$ means:

either of the $2$ integers is even or either of the $2$ integers is prime.

### Defective Devices

Consider the experiment $\EE$ such that $3$ devices are checked as to whether they are operational.

Let $A$ be the event that at least $1$ of these $3$ devices is defective.

Let $B$ be the event that all $3$ devices are sound.

Then their union $A \cup B$ is a certainty.

## Also see

• Results about unions of events can be found here.