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An event is any subset of the [[Sample space]].
Example: Given
$$S = \{1,2,3,4,5,6\}$$
then
$$A = \{2,4\}$$
is an event.
Can be visualized with [[Venn diagram]]s.
Events happen with a [[Probability]].
## Special events
Some special events are the empty event ($\phi$) and the [[Sample space]] itself ($S$).
# Operations
Just like there are normal operations (+, \*, ..) on numbers there exist
operations on events. They work much like events on normal [[Set]]s.
## Intersection
$$A \cap B$$
## Union
$$A \cup B$$
## Complement
$$A'$$
# Disjoint
Two events are disjoint if they don't "overlap" in any way.
# Independent
Two events are independent if $P(A \cap B) = P(A) \cdot P(B)$.
Intuition: $A$ does not affect $B$ and vice versa.
$(A, B)$ independent $\Leftrightarrow$ $(A', B)$ independent.
For example, given a fair dice roll and
$$A = \{2\}, \ B = \{2, 3\}, \ C = S$$
then $A$ and $B$ are dependent but $A$ and $C$ are independent (since the
outcome of $A$ doesn't affect the outcome of $C$ since $P(C) = 1$.
In general, $A_1, ..., A_n$ are independent if...
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