From c4950dfb23d1fe8cca7cb523d9ae4ea4b4dda2d5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Gustav=20S=C3=B6rn=C3=A4s?= <gustav@sornas.net>
Date: Fri, 21 Jan 2022 13:28:45 +0100
Subject: move files

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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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