From d50e6bd54735d292de72e1b1365c1780530760dd Mon Sep 17 00:00:00 2001 From: Janis Hutz Date: Mon, 3 Aug 2026 08:30:27 +0200 Subject: [PATCH] [AW] Fix error in multiplication rule, fixes #9 --- .../algorithms-and-probability/aw-summary.pdf | Bin 1053997 -> 1054122 bytes .../algorithms-and-probability/aw-summary.tex | 4 +--- .../probability/conditional-probability.tex | 2 +- 3 files changed, 2 insertions(+), 4 deletions(-) diff --git a/semester2/algorithms-and-probability/aw-summary.pdf b/semester2/algorithms-and-probability/aw-summary.pdf index 1f94488d9b0ba9b4f8f42b9a9c5ad7f52c8ceee9..8e0e353c82939c64609ea9ff9e28e4394877a3d9 100644 GIT binary patch delta 207588 zcmV)NK)1iGsz9o%K(H$i0Wy;j0x5r;Rm*PEKos5kD@Lp)QazdXqY{fET1sJ2NEU^( z3pa5SS9KEn5R|Xyj%N~*)Ip+)#8>0{I(N=Jrf7~R`jEUEC<Dkt0rXjm8g1I-;pY z#!2FgLgN{l;IpUssw$dASr1Yn1kRQ-Z%BMyt?ma5XZOWZ(G0l3&x5=16_S6DghBo; z_$pf#G48T$etU=He4PA9yaz?>Z$(C!b!b{9lRJuL@a_sxBAi7(JI@k4HKAI7{e(uz 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-\input{\dir/include.tex} -\load{recommended} +\input{~/projects/latex/old/janishutz-helpers-v1.tex} \setup{Algorithms and Probability} diff --git a/semester2/algorithms-and-probability/parts/probability/conditional-probability.tex b/semester2/algorithms-and-probability/parts/probability/conditional-probability.tex index ea5fdfb..633ab19 100644 --- a/semester2/algorithms-and-probability/parts/probability/conditional-probability.tex +++ b/semester2/algorithms-and-probability/parts/probability/conditional-probability.tex @@ -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}

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