{
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  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Think Bayes\n",
    "\n",
    "This notebook presents example code and exercise solutions for Think Bayes.\n",
    "\n",
    "Copyright 2018 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import classes from thinkbayes2\n",
    "from thinkbayes2 import Hist, Pmf, Suite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** This exercise is from one of my favorite books, David MacKay's \"Information Theory, Inference, and Learning Algorithms\":\n",
    "\n",
    "> Elvis Presley had a twin brother who died at birth.  What is the probability that Elvis was an identical twin?\"\n",
    "    \n",
    "To answer this one, you need some background information: According to the Wikipedia article on twins:  \"Twins are estimated to be approximately 1.9% of the world population, with monozygotic twins making up 0.2% of the total---and 8% of all twins.''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Pmf({'fraternal': 0.92, 'identical': 0.08})"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's a Pmf with the prior probability that Elvis \n",
    "# was an identical twin (taking the fact that he was a \n",
    "# twin as background information)\n",
    "\n",
    "pmf = Pmf(dict(fraternal=0.92, identical=0.08))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "fraternal 0.8518518518518517\n",
      "identical 0.14814814814814814\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And here's the update.  The data is that the other twin\n",
    "# was also male, which has likelihood 1 if they were identical\n",
    "# and only 0.5 if they were fraternal.\n",
    "\n",
    "pmf['fraternal'] *= 0.5\n",
    "pmf['identical'] *= 1\n",
    "pmf.Normalize()\n",
    "pmf.Print()"
   ]
  }
 ],
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