diff --git a/is/UB1/ISUB1.pdf b/is/UB1/ISUB1.pdf
index 7b25945..2a82d91 100644
--- a/is/UB1/ISUB1.pdf
+++ b/is/UB1/ISUB1.pdf
Binary files differ
diff --git a/is/UB1/ISUB1.tex b/is/UB1/ISUB1.tex
index a00a05a..71831be 100644
--- a/is/UB1/ISUB1.tex
+++ b/is/UB1/ISUB1.tex
@@ -95,36 +95,34 @@
                 one pair:\\
                 ${13\choose 1}{3\choose 2}{12 \choose 3}\cdot 3^3=231660$\\
                 $\mathds{P}(1\ pair|\neg Spades)=\frac{231660}{575757}=\frac{1980}{4921}\approx 0.402$
-                \item $A:=2\ pairs,\ B:=\neg Spades$\\
+                \item $A:=1\ pair,\ B:=\neg Spades$\\
                 $P(A|B)=\frac{P(B|A)P(A)}{P(B)}$\\
-                $P(A)=\frac{198}{4165},\ P(B)=\frac{39}{52}\cdot\frac{38}{51}\cdot\frac{37}{50}\cdot\frac{36}{49}\cdot\frac{35}{48}=\frac{2109}{9520}$\\
+                $P(A)=\frac{352}{833},\ P(B)=\frac{39}{52}\cdot\frac{38}{51}\cdot\frac{37}{50}\cdot\frac{36}{49}\cdot\frac{35}{48}=\frac{2109}{9520}$\\
                 $P(B|A)=1-P(\neg B| A)=1-\left(\frac{1}{4}+\frac{3}{4}\frac{1}{4}+\left(\frac{3}{4}\right)^2\frac{1}{4}+\left(\frac{3}{4}\right)^3\frac{1}{4}+\left(\frac{3}{4}\right)^4\frac{1}{3}\right)=1-\frac{101}{128}=\frac{27}{128}\approx 0.211$\\
-                $P(A|B)=\frac{\frac{27}{128}\cdot \frac{198}{4165}}{\frac{2109}{9520}}=\frac{891}{19684}\approx 0.0452$%TODO
+                $P(A|B)=\frac{\frac{27}{128}\cdot \frac{352}{833}}{\frac{2109}{9520}}=\frac{1980}{4921}\approx 0.0402$%TODO
             \end{enumerate}
         \end{enumerate}
     \Aufgabe{Random Variables}{2+2+2=6}
         \begin{enumerate}
             \item $F\left(\frac{3}{2}\right)-F\left(\frac{1}{2}\right)=\frac{3}{4}-\frac{1}{4}=\frac{1}{2}$
-            \item $x^2<x\Leftrightarrow x\in(0,1)$  doesn't work if the pdf is something like x+a\\
-            $\Rightarrow \mathds{P}(Y<X)=\mathds{P}(0<X<1)=F\left(1\right)-F\left(0\right)=\frac{1}{2}-0=\frac{1}{2}$\\
-            $f_x(x)=\begin{cases}
+            \item $f_X(x)=\begin{cases}
             0 & if\ x<0\ or\ x>2\\
             \frac{1}{2} & if\ 0\leq x\leq 2\\
             \end{cases}$
-             $f_y(x)=\begin{cases}
+             $f_Y(x)=\begin{cases}
              0 & if\ x<0\ or\ x>2\\
              \frac{1}{2}x & if\ 0\leq x\leq 2\\
              \end{cases}$\\\\
-             $f_y(x)<f_x(x) \Leftrightarrow x\in[0,1)$ \\
+             $f_Y(x)<f_X(x) \Leftrightarrow x\in (0,1)$ \\
              $\Rightarrow \mathds{P}(Y<X)=\mathds{P}(0\leq X<1)=F\left(1\right)-F\left(0\right)=\frac{1}{2}-0=\frac{1}{2}$\\
             \item $F_Z(x)=\begin{cases}
                 0 & if\ x<0\\
                 \frac{\sqrt{2}}{2}\sqrt{x} & if\ 0\leq x\leq 2\\
                 1 & if\ x>2
-            \end{cases}$%TODO
+            \end{cases}$
         \end{enumerate}
     \Aufgabe{Keep Rolling!}{4}
         $\mathds{E}(X)=\frac{1}{\frac{1}{6}}=6$ (geometric distribution)\\
-        $\mathds{E}(X)=?$%TODO
+        $\mathds{E}(X)=?$%TODO: Explain
 \end{document}