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\begin{expandtable}
\begin{tabularx}{\linewidth}{|LIR|}
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\multicolumn{2}{|c|}{
Wahrscheinlichkeitstheorie ($A,B$ Ereignisse und $X,Y$ Variablen)
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$\E(X + Y) = \E(X) + \E(Y)$ & $\Pr[A \vert B] = \frac{\Pr[A \land B]}{\Pr[B]}$ \\
$\E(\alpha X) = \alpha \E(X)$ & $\Pr[A \lor B] = \Pr[A] + \Pr[B] - \Pr[A \land B]$ \\
$X, Y$ unabh. $\Leftrightarrow \E(XY) = \E(X) \cdot \E(Y)$ & $A, B$ disj. $\Leftrightarrow \Pr[A \land B] = \Pr[A] \cdot \Pr[B]$\\
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\end{tabularx}
\begin{tabularx}{\linewidth}{|Xlr|lrX|}
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\multicolumn{6}{|c|}{\textsc{Bertrand}'s Ballot Theorem (Kandidaten $A$ und $B$, $k \in \mathbb{N}$)} \\
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& $\#A > k\#B$ & $Pr = \frac{a - kb}{a + b}$ &
$\#B - \#A \leq k$ & $Pr = 1 - \frac{a!b!}{(a + k + 1)!(b - k - 1)!}$ & \\
& $\#A \geq k\#B$ & $Pr = \frac{a + 1 - kb}{a + 1}$ &
$\#A \geq \#B + k$ & $Num = \frac{a - k + 1 - b}{a - k + 1} \binom{a + b - k}{b}$ & \\
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\end{tabularx}
\end{expandtable}
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