diff --git a/is/UB1/ISUB1.tex b/is/UB1/ISUB1.tex
index ee651c8..1f51ce3 100644
--- a/is/UB1/ISUB1.tex
+++ b/is/UB1/ISUB1.tex
@@ -89,11 +89,12 @@
             \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 hands with exaclty two pairs without spades: ${13\choose 2}{3\choose 2}^2\cdot 11\cdot 3=23166$\\
+                possible hands ${39 \choose 5} = 575757$\\
+                $\mathds{P}(2\ pairs|\neg Spades)=\frac{23166}{575757}=\frac{198}{4921}\approx 0.04023$\\
                 one pair:\\
                 ${13\choose 1}{3\choose 2}{12 \choose 3}\cdot 3^3=231660$\\
-                $\mathds{P}(1\ pair|\neg Spades)=\frac{231660}{2598960}=\frac{297}{3332}\approx 0.0891$
+                $\mathds{P}(1\ pair|\neg Spades)=\frac{231660}{575757}=\frac{1980}{4921}\approx 0.40235$
                 \item $A:=2\ pairs,\ B:=\neg Spades$\\
                 $P(A|B)=\frac{P(B|A)P(A)}{P(B)}$\\
                 $P(A)=\frac{198}{4165},\ P(B)=\frac{39}{52}\cdot\frac{38}{51}\cdot\frac{37}{50}\cdot\frac{36}{49}\cdot\frac{35}{48}=\frac{2109}{9520}$\\
@@ -104,8 +105,18 @@
     \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 $x^2<x\Leftrightarrow x\in(0,1)$\\
-            $\Rightarrow \mathds{P}(Y<X)=\mathds{P}(0<X<1)=F\left(1\right)-F\left(0\right)=\frac{1}{2}-0=\frac{1}{2}$
+            \item $x^2<x\Leftrightarrow x\in(0,1)$  doesn't work if the pdf is something like x+a\\
+            $\Rightarrow \mathds{P}(Y<X)=\mathds{P}(0<X<1)=F\left(1\right)-F\left(0\right)=\frac{1}{2}-0=\frac{1}{2}$\\
+            $f_x(x)=\begin{cases}
+            0 & if\ x<0\ or\ x>2\\
+            \frac{1}{2} & if\ 0\leq x\leq 2\\
+            \end{cases}$
+             $f_y(x)=\begin{cases}
+             0 & if\ x<0\ or\ x>2\\
+             \frac{1}{2}x & if\ 0\leq x\leq 2\\
+             \end{cases}$\\\\
+             $f_y(x)<f_x(x) \Leftrightarrow x\in[0,1)$ \\
+             $\Rightarrow \mathds{P}(Y<X)=\mathds{P}(0\leq X<1)=F\left(1\right)-F\left(0\right)=\frac{1}{2}-0=\frac{1}{2}$\\
             \item $F_Z(x)=\begin{cases}
                 0 & if\ x<0\\
                 \frac{\sqrt{2}}{2}\sqrt{x} & if\ 0\leq x\leq 2\\