diff --git a/is/UB1/ISUB1.tex b/is/UB1/ISUB1.tex index f2f73da..59bd46b 100644 --- a/is/UB1/ISUB1.tex +++ b/is/UB1/ISUB1.tex @@ -6,7 +6,7 @@ \usepackage[utf8]{inputenc} %Umlaute & Co \usepackage{hyperref} %Links \usepackage{ifthen} %ifthenelse - +\usepackage{enumerate} \usepackage{algpseudocode} %Pseudocode \usepackage{dsfont} % schöne Zahlenräumezeichen @@ -55,9 +55,9 @@ \end{minipage} \vspace{1cm} \begin{center} -{\Large\bf Blatt #1} +{\Large\bf Sheet #1} -{(Abgabe #3)} +{(Hand in #3)} \end{center} } @@ -74,21 +74,33 @@ \else \fi -\indent\textbf{Execise \arabic{n}: #1} (#2 Punkte)\\} +\indent\textbf{Exercise \arabic{n}: #1} (#2 Punkte)\\} \begin{document} %\header{BlattNr}{Tutor}{Abgabedatum}{Vorlesungsname}{Namen}{Semester}{Anzahl Aufgaben} - \header{1}{}{2015-04-22}{Intelligent Systems}{\textit{Maximus Mutschler}\\ \textit{Jan-Peter Hohloch} + \header{1}{}{2015-04-22}{Intelligent Systems I}{\textit{Maximus Mutschler}\\ \textit{Jan-Peter Hohloch} }{SS 15}{4} \vspace{1cm} \Aufgabe{Python}{4} done - \Aufgabe{Poker} + \Aufgabe{Poker}{2+2+4=8} \begin{enumerate}[1.] - \item + \item possible hands: ${52 \choose 5}=2598960$\\ + hands with exaclty one pair: ${13\choose 1}\cdot{4\choose 2}\cdot {12\choose 3}\cdot 4^3=1098240$\\ + $\mathds{P}(1\ pair)=\frac{1098240}{2598960}=\frac{352}{833}\approx 0.423$ + \item hands with exaclty two pairs: ${13\choose 2}{4\choose 2}^2\cdot 11\cdot 4=123552$\\ + $\mathds{P}(2\ pairs)=\frac{123552}{2598960}=\frac{198}{4165}\approx 0.0475$ + \item \begin{enumerate}[(a)] + \item hands with exaclty two pairs without Spades: ${13\choose 2}{3\choose 2}^2\cdot 11\cdot 3=23166$\\ + $\mathds{P}(2\ pairs|\neg Spades)=\frac{23166}{2598960}=\frac{297}{33320}\approx 0.00891$ + \item $A:=2\ pairs,\ B:=\neg Spades$\\ + $P(A|B)=\frac{P(B|A)P(A)}{P(B)}$\\ + $P(A)=\frac{198}{4165},\ P(B)=\frac{39}{52}\cdot\frac{38}{51}\cdot\frac{37}{50}\cdot\frac{36}{49}\cdot\frac{35}{48}=\frac{2109}{9520}$\\ + $P(B|A)=?$%TODO + \end{enumerate} \end{enumerate} \end{document}