diff --git a/Lectures_my/EMPP/Lecture1/mchrzasz.tex b/Lectures_my/EMPP/Lecture1/mchrzasz.tex
index f58acc8..c03e7dc 100644
--- a/Lectures_my/EMPP/Lecture1/mchrzasz.tex
+++ b/Lectures_my/EMPP/Lecture1/mchrzasz.tex
@@ -564,6 +564,47 @@
 \end{footnotesize}
 \end{frame}
 
+
+\begin{frame}\frametitle{Buffon needle, $\rm \color{RubineRed}{Lecture1/Heads\_tails}$  }
+\begin{small}
+
+
+$\Rrightarrow$ Lets make this toy experiment and calculate the $\pi$ number.\\
+$\hookrightarrow$ We can simulate the central position $(y)$ of an needle between $(-L, L)$ from $\mathcal{U}(-L, L)$. 
+
+  \begin{exampleblock}{Symmetry:}                                                                                                                                                                                                                                                                                                
+Please note the symmetry of the problem, if the position of the needle would be $>L$ then we can shift the needle by any number of $L$'s.
+        \end{exampleblock} 
+
+$\hookrightarrow$ New we simulate the angle $(\phi)$ with a flat distribution from $(0,\pi)$. 
+$\hookrightarrow$ The maximum and minimum $y$ position of the needle are:
+\begin{align*}
+y_{\max}=y+\vert \cos \phi \vert l\\
+y_{\min}=y-\vert \cos \phi \vert l
+\end{align*}
+$\hookrightarrow$ Now we check if the needle touches any of the lines: $y=L$, $y=0$ or $y=-L$. If yes we count the events.
+\end{small}
+\begin{center}
+
+
+\begin{footnotesize}
+
+
+\begin{tabular}{r c c c }
+$N$ & $\hat{\pi}$ & $\hat{\pi} - \pi$ & $\sigma(\hat{\pi})$ \\
+10000 & $3.12317$ & $-0.01842$ & $0.03047$\\
+100000 & $3.14707$ & $0.00547$ & $0.00979$\\
+1000000 & $3.13682$ & $-0.00477$ & $0.00307$\\
+10000000 & $3.14096$ & $-0.00063$ & $0.00097$\\
+
+
+\end{tabular}
+
+\end{footnotesize}
+\end{center}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
 \begin{frame}\frametitle{Central Limit Theorem}
 \begin{footnotesize}
     \begin{exampleblock}{}                                                                                                                                                                                                                                                                                                
diff --git a/Lectures_my/EMPP/MC_examples/CLT/dupa.png b/Lectures_my/EMPP/MC_examples/CLT/dupa.png
new file mode 100644
index 0000000..70db5f7
--- /dev/null
+++ b/Lectures_my/EMPP/MC_examples/CLT/dupa.png
Binary files differ
diff --git a/Lectures_my/EMPP/MC_examples/CLT/ht.py b/Lectures_my/EMPP/MC_examples/CLT/ht.py
new file mode 100644
index 0000000..bfa1be7
--- /dev/null
+++ b/Lectures_my/EMPP/MC_examples/CLT/ht.py
@@ -0,0 +1,31 @@
+from ROOT import  * 
+import sys
+
+def main(argv=sys.argv):  
+
+
+    pi=3.14159265359
+    c=TCanvas("c1", "c1", 800,600)
+ 
+    NTOYS=1000000
+    rand=TRandom(123)    
+
+    hists=[]
+
+    for i in range(1,13, 2):
+        hist=TH1D("hist", "hist", 400, 0, 10)
+        for j in range(0, NTOYS):
+            tmp=0.
+            for k in range(0,i):
+                tmp+=rand.Rndm()
+            hist.Fill(tmp)
+        hists.append(hist)
+
+    for i in range(0,len(hists)): 
+        if(i==0): hists[i].DrawNormalized()
+        else: hists[i].DrawNormalized("SAME")
+
+    c.SaveAs("dupa.png")
+
+if __name__ == "__main__":    
+    sys.exit(main())      
diff --git a/Lectures_my/EMPP/MC_examples/CLT/ht.py~ b/Lectures_my/EMPP/MC_examples/CLT/ht.py~
new file mode 100644
index 0000000..d9f4fdf
--- /dev/null
+++ b/Lectures_my/EMPP/MC_examples/CLT/ht.py~
@@ -0,0 +1,31 @@
+from ROOT import  * 
+import sys
+
+def main(argv=sys.argv):  
+
+
+    pi=3.14159265359
+    c=TCanvas("c1", "c1", 800,600)
+ 
+    NTOYS=10000
+    rand=TRandom(123)    
+
+    hists=[]
+
+    for i in range(1,13, 2):
+        hist=TH1D("hist", "hist", 400, 0, 10)
+        for j in range(0, NTOYS):
+            tmp=0.
+            for k in range(0,i):
+                tmp+=rand.Rndm()
+            hist.Fill(tmp)
+        hists.append(hist)
+
+    for i in range(0,len(hists)): 
+        if(i==0): hists[i].DrawNormalized()
+        else: hists[i].DrawNormalized("SAME")
+
+    c.SaveAs("dupa.png")
+
+if __name__ == "__main__":    
+    sys.exit(main())      
diff --git a/Lectures_my/EMPP/MC_examples/Heads_tails/ht.py b/Lectures_my/EMPP/MC_examples/Heads_tails/ht.py
deleted file mode 100644
index fcb8078..0000000
--- a/Lectures_my/EMPP/MC_examples/Heads_tails/ht.py
+++ /dev/null
@@ -1,23 +0,0 @@
-from ROOT import  * 
-import sys
-
-def main(argv=sys.argv):  
-
-
-    pi=3.14159265359
-    c=TCanvas("c1", "c1", 800,600)
-    fun=TF1("f1", "0.9*cos(x)", 0, pi/2)
-    fun.SetLineColor(kBlack)
-    fun.SetFillColor(1)
-    fun.SetTitle("")
-    fun.GetXaxis().SetTitle('x')  
-    fun.GetYaxis().SetTitle('y')
-
-    fun.Draw("FC")
-
-    c1.SaveAs("result.png")
-        
-
-
-if __name__ == "__main__":    
-    sys.exit(main())      
diff --git a/Lectures_my/EMPP/MC_examples/Heads_tails/ht.py~ b/Lectures_my/EMPP/MC_examples/Heads_tails/ht.py~
deleted file mode 100644
index b9852a4..0000000
--- a/Lectures_my/EMPP/MC_examples/Heads_tails/ht.py~
+++ /dev/null
@@ -1,22 +0,0 @@
-from ROOT import  * 
-import sys
-
-def main(argv=sys.argv):  
-
-
-    pi=3.14159265359
-    c=TCanvas("c1", "c1", 800,600)
-    fun=TF1("f1", "0.9*cos(x)", 0, pi/2)
-    fun.SetLineColor(kBlack)
-    fun.SetFillColor(1)
-    fun.SetTitle("")
-    fun.GetXaxis().SetTitle('x')  
-
-    fun.Draw("FC")
-
-    c1.SaveAs("result.png")
-        
-
-
-if __name__ == "__main__":    
-    sys.exit(main())      
diff --git a/Lectures_my/EMPP/MC_examples/Heads_tails/ht_MC.py b/Lectures_my/EMPP/MC_examples/Heads_tails/ht_MC.py
new file mode 100644
index 0000000..33d131c
--- /dev/null
+++ b/Lectures_my/EMPP/MC_examples/Heads_tails/ht_MC.py
@@ -0,0 +1,44 @@
+from ROOT import  * 
+import sys
+
+def main(argv=sys.argv):
+    ntoys=[10000,100000, 1000000, 10000000]
+    for i in ntoys:
+        calc_pi(i)
+
+def calc_pi(NTOYS):
+
+    # seting up dimensions
+    L=1
+    l=0.8
+    pi=3.14159265359
+    rand=TRandom3(12)
+    # the lines on the table are at ..,-2L, -L, 0, L, 2L,...
+    counter=0.
+    
+    
+    
+    for i in range(NTOYS):
+        rand_y=rand.Rndm()-0.5 # this is in range (-0.5,0.5)
+        rand_y=rand_y*2.*L # now we have range -L, L
+        rand_angle=rand.Rndm()
+        rand_angle=rand_angle*pi # this is the angle in range(0,pi)
+        delta_y=(l/2)*cos(rand_angle)
+        y_max=rand_y+abs(delta_y)
+        y_min=rand_y-abs(delta_y) 
+        if(y_max>L or y_min<-L): counter=counter+1. 
+        if(y_max>0 and y_min<0): counter=counter+1.
+
+
+    counter=counter/NTOYS
+    #now remember P=2l/piL, so:
+    Pi=2*l/(L*counter)
+    counter_err=(1./sqrt(NTOYS))*sqrt(counter*(1.-counter))
+    pi_err=(counter_err/counter)*Pi
+
+    print NTOYS , round(Pi,5), round(Pi-pi,5), round(pi_err,5)
+
+
+
+if __name__ == "__main__":    
+    sys.exit(main())      
diff --git a/Lectures_my/EMPP/MC_examples/Heads_tails/ht_plot.py b/Lectures_my/EMPP/MC_examples/Heads_tails/ht_plot.py
new file mode 100644
index 0000000..fcb8078
--- /dev/null
+++ b/Lectures_my/EMPP/MC_examples/Heads_tails/ht_plot.py
@@ -0,0 +1,23 @@
+from ROOT import  * 
+import sys
+
+def main(argv=sys.argv):  
+
+
+    pi=3.14159265359
+    c=TCanvas("c1", "c1", 800,600)
+    fun=TF1("f1", "0.9*cos(x)", 0, pi/2)
+    fun.SetLineColor(kBlack)
+    fun.SetFillColor(1)
+    fun.SetTitle("")
+    fun.GetXaxis().SetTitle('x')  
+    fun.GetYaxis().SetTitle('y')
+
+    fun.Draw("FC")
+
+    c1.SaveAs("result.png")
+        
+
+
+if __name__ == "__main__":    
+    sys.exit(main())      
diff --git a/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/dupa.png b/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/dupa.png
deleted file mode 100644
index 70db5f7..0000000
--- a/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/dupa.png
+++ /dev/null
Binary files differ
diff --git a/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/ht.py b/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/ht.py
deleted file mode 100644
index bfa1be7..0000000
--- a/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/ht.py
+++ /dev/null
@@ -1,31 +0,0 @@
-from ROOT import  * 
-import sys
-
-def main(argv=sys.argv):  
-
-
-    pi=3.14159265359
-    c=TCanvas("c1", "c1", 800,600)
- 
-    NTOYS=1000000
-    rand=TRandom(123)    
-
-    hists=[]
-
-    for i in range(1,13, 2):
-        hist=TH1D("hist", "hist", 400, 0, 10)
-        for j in range(0, NTOYS):
-            tmp=0.
-            for k in range(0,i):
-                tmp+=rand.Rndm()
-            hist.Fill(tmp)
-        hists.append(hist)
-
-    for i in range(0,len(hists)): 
-        if(i==0): hists[i].DrawNormalized()
-        else: hists[i].DrawNormalized("SAME")
-
-    c.SaveAs("dupa.png")
-
-if __name__ == "__main__":    
-    sys.exit(main())      
diff --git a/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/ht.py~ b/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/ht.py~
deleted file mode 100644
index d9f4fdf..0000000
--- a/Lectures_my/EMPP/MC_examples/Large_Number_Theorem/ht.py~
+++ /dev/null
@@ -1,31 +0,0 @@
-from ROOT import  * 
-import sys
-
-def main(argv=sys.argv):  
-
-
-    pi=3.14159265359
-    c=TCanvas("c1", "c1", 800,600)
- 
-    NTOYS=10000
-    rand=TRandom(123)    
-
-    hists=[]
-
-    for i in range(1,13, 2):
-        hist=TH1D("hist", "hist", 400, 0, 10)
-        for j in range(0, NTOYS):
-            tmp=0.
-            for k in range(0,i):
-                tmp+=rand.Rndm()
-            hist.Fill(tmp)
-        hists.append(hist)
-
-    for i in range(0,len(hists)): 
-        if(i==0): hists[i].DrawNormalized()
-        else: hists[i].DrawNormalized("SAME")
-
-    c.SaveAs("dupa.png")
-
-if __name__ == "__main__":    
-    sys.exit(main())