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[AW] Fix error in multiplication rule, fixes #9

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janishutz
2026-08-03 08:30:27 +02:00
parent ea54c5a249
commit d50e6bd547
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semester2/algorithms-and-probability/parts/probability/conditional-probability.tex
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@@ -16,7 +16,7 @@
\begin{theorem}[]{Multiplication law}
Let $A_1, \ldots, A_n$ be events. If $\Pr[A_1 \cap \ldots \cap A_n] > 0$, we have
\[
\Pr[A_1 \cap \ldots \cap A_n] = \Pr[A_1] \cdot \Pr[A_2|A_1] \cdot \Pr[A_3|A_1 \cap A_2] \cdot \ldots \cdot \Pr[A_n|A_1 \cap \ldots \cap A_n]
\Pr[A_1 \cap \ldots \cap A_n] = \Pr[A_1] \cdot \Pr[A_2|A_1] \cdot \Pr[A_3|A_1 \cap A_2] \cdot \ldots \cdot \Pr[A_n|A_1 \cap \ldots \cap A_{n - 1}]
\]
\end{theorem}