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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
3 changed files with 2 additions and 4 deletions
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semester2/algorithms-and-probability/aw-summary.pdf
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semester2/algorithms-and-probability/aw-summary.tex
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@@ -1,9 +1,7 @@
\documentclass{article} \documentclass{article}
\newcommand{\dir}{~/projects/latex} \input{~/projects/latex/old/janishutz-helpers-v1.tex}
\input{\dir/include.tex}
\load{recommended}
\setup{Algorithms and Probability} \setup{Algorithms and Probability}
semester2/algorithms-and-probability/parts/probability/conditional-probability.tex
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@@ -16,7 +16,7 @@
\begin{theorem}[]{Multiplication law} \begin{theorem}[]{Multiplication law}
Let $A_1, \ldots, A_n$ be events. If $\Pr[A_1 \cap \ldots \cap A_n] > 0$, we have 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} \end{theorem}