diff --git a/semester2/algorithms-and-probability/aw-summary.pdf b/semester2/algorithms-and-probability/aw-summary.pdf index 1f94488..8e0e353 100644 Binary files a/semester2/algorithms-and-probability/aw-summary.pdf and b/semester2/algorithms-and-probability/aw-summary.pdf differ diff --git a/semester2/algorithms-and-probability/aw-summary.tex b/semester2/algorithms-and-probability/aw-summary.tex index 6bc3725..61f510a 100644 --- a/semester2/algorithms-and-probability/aw-summary.tex +++ b/semester2/algorithms-and-probability/aw-summary.tex @@ -1,9 +1,7 @@ \documentclass{article} -\newcommand{\dir}{~/projects/latex} -\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}