added quick simulation to BanachMatchbox.ipynb

Author: unpingco

BanachMatchbox.ipynb

@@ -424,7 +424,36 @@
     "\n",
     "Finally, for $P_7$, we have the following:\n",
     "\n",
-    "$$ P_7 = p_7 (1-P_4)(1-p_5)(1-p_6) = 1\\frac{7}{8}\\frac{5}{7}\\frac{1}{2} =\\frac{5}{16}$$\n"
+    "$$ P_7 = p_7 (1-P_4)(1-p_5)(1-p_6) = 1\\frac{7}{8}\\frac{5}{7}\\frac{1}{2} =\\frac{5}{16}$$\n",
+    "\n",
+    "Note that\n",
+    "\n",
+    "$$ P_4+P_5+P_6+P_7 = 1 $$\n",
+    "\n",
+    "A quick simulation can bear this out. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 53,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "Counter({4: 130, 5: 276, 6: 288, 7: 306})"
+      ]
+     },
+     "execution_count": 53,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from collections import Counter\n",
+    "Counter([len(tuple(step())) for i in range(1000)])"
    ]
   },
   {