From 802c3d64d2402c5bf060fb5488bd10688d2a6965 Mon Sep 17 00:00:00 2001
From: Julian T <julian@jtle.dk>
Date: Fri, 4 Jun 2021 13:00:07 +0200
Subject: Add more changes to dig and prob

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 sem6/prob/eksamnen/notes.tex | 47 --------------------------------------------
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-\title{Eksamnens Noter}
-
-
-The universal set or sample space is the set everything, and is denoted $S$.
-Therefore the probability of hitting $S$ is $P(S) = 1$.
-
-This is the first of 3 axioms repeated below.
-
-\begin{enumerate}
-    \item For any event $A$, $P(A) \geq 0$.
-    \item The probability of hitting sample space is always 1, $P(S) = 1$.
-    \item If events $A_1, A_2, ...$ are \textbf{disjoint} event, then
-        \begin{equation}
-            P(A_1 \cup A_2 ...) = P(A_1) + P(A_2)\,.
-        \end{equation}
-\end{enumerate}
-
-The last axiom requires that the events $A_n$ are disjoint.
-If they aren't one should subtract the part they have in common.
-This is called the \emph{Inclusion-Exclusion Principle}.
-
-\begin{principle}
-    The \emph{Inclusion-Exclusion Principle} is defined as
-    \begin{equation}
-        P(A \cup B) = P(A) + P(B) - P(A \cap B)\,.
-    \end{equation}
-    Definition with 3 events can be found in the in the book.
-\end{principle}
-
-\section{Counting}
-
-The probability of a event $A$ can be found by
-\begin{equation}
-    P(A) = \frac {|A|} {|S|}\,.
-\end{equation}
-It is therefore required to count how many elements are in $S$ and $A$.
-The most simple method is the \emph{multiplication principle}.
-
-\begin{principle}[Multiplication principle]
-    Let there be $r$ random experiments, where the $k$'th experiment has $n_k$ outcomes.
-    Then there are
-    \begin{equation}
-        n_1 \cdot n_2 \cdot ... \cdot n_r
-    \end{equation}
-    possible outcomes over all $r$ experiments.
-\end{principle}
-
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