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 $\omega \in A \cap B$, where $A \cap B$ denotes the intersection of $A$ and $B$.
Then both $A$ and $B$ occur.
Also denoted as
Some sources denote the occurrence of both $A$ and $B$ as $A B$.
Then their intersections $A \cap B$ means:
That is, either:
- Definition:Union of Events
- Definition:Difference of Events
- Definition:Symmetric Difference of Events
- Results about intersections of events can be found here.
- 1965: A.M. Arthurs: Probability Theory ... (previous) ... (next): Chapter $2$: Probability and Discrete Sample Spaces: $2.2$ Sample spaces and events
- 1968: A.A. Sveshnikov: Problems in Probability Theory, Mathematical Statistics and Theory of Random Functions (translated by Richard A. Silverman) ... (previous) ... (next): $\text I$: Random Events: $1$. Relations among Random Events
- 1986: Geoffrey Grimmett and Dominic Welsh: Probability: An Introduction ... (previous) ... (next): $1$: Events and probabilities: $1.2$: Outcomes and events