{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Who will be the Mormon prophet in year 2028?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary October 3, 2015\n",
    "\n",
    "  * Method 1: Winner takes all predicts Dallin H. Oaks\n",
    "  * Method 2: Monte-Carlo simulation predicts Jeffery R. Holland with an approx. 25% chance.\n",
    "  * Method 3: Subjectively adjusted health predicts Dallin H. Oaks with an approx. 28% chance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary January 1, 2018\n",
    "\n",
    "  * Method 1: Winner takes all predicts David A. Bednar in 2028 and Russle M. Nelson lives to 2020\n",
    "  * Method 2: Monte-Carlo simulation predicts David A. Bednar in 2028 with approx. 26% chance and Russle M. Nelson lives to 2020 with an approx. 42% chance.\n",
    "  * Method 3: Subjectively adjusted health predicts Other in 2028 with approx. 99% chance and Russle M. Nelson lives to 2022 with approx. 25% chance.\n",
    "\n",
    "## Notes\n",
    "  \n",
    "  * Adds qgrid dependency"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It just so happens that there's a a convenient pattern to whom is usually called to be the next prophet of *The Church of Jesus Christ of Latter-day Saints*. For most of the 20th century and all of the 21st century so far, the pattern has been that the prophet of the church is the most senior apostle (by date of calling to the Quorum of the Twelve) becomes the prophet when the previous prophet dies. There are 15 of these apostles at any given time: three in the \"First Presidency\", comprising the prophet and his two counselors, and twelve in the Quorum of the Twelve Apostles.\n",
    "\n",
    "Given the ages of the apostles and some average actuarial life tables (which we use here despite knowing that these men are generally far healthier than the average population), we can fairly easily calculate the likely age of death of the current apostles and rank them by seniority to find some likely scenarios for new prophets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rcParams\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import qgrid as qg\n",
    "from datetime import datetime, timedelta\n",
    "from collections import defaultdict\n",
    "import seaborn as sns\n",
    "rcParams['figure.figsize'] = (10.0, 2.0)\n",
    "sns.set(style=\"darkgrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "now = datetime.now()\n",
    "CURRENT_YEAR = now.year"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we load some actuarial life tables which give the population-level probability of death at any particular age."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>M</th>\n",
       "      <th>F</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Age</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>0.061620</td>\n",
       "      <td>0.043899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>0.068153</td>\n",
       "      <td>0.048807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>0.075349</td>\n",
       "      <td>0.054374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>0.083230</td>\n",
       "      <td>0.060661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.091933</td>\n",
       "      <td>0.067751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>85</th>\n",
       "      <td>0.101625</td>\n",
       "      <td>0.075729</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86</th>\n",
       "      <td>0.112448</td>\n",
       "      <td>0.084673</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>87</th>\n",
       "      <td>0.124502</td>\n",
       "      <td>0.094645</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>88</th>\n",
       "      <td>0.137837</td>\n",
       "      <td>0.105694</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>89</th>\n",
       "      <td>0.152458</td>\n",
       "      <td>0.117853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>90</th>\n",
       "      <td>0.168352</td>\n",
       "      <td>0.131146</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>91</th>\n",
       "      <td>0.185486</td>\n",
       "      <td>0.145585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>92</th>\n",
       "      <td>0.203817</td>\n",
       "      <td>0.161175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>93</th>\n",
       "      <td>0.223298</td>\n",
       "      <td>0.177910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>94</th>\n",
       "      <td>0.243867</td>\n",
       "      <td>0.195774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>95</th>\n",
       "      <td>0.264277</td>\n",
       "      <td>0.213849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>96</th>\n",
       "      <td>0.284168</td>\n",
       "      <td>0.231865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>0.303164</td>\n",
       "      <td>0.249525</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>0.320876</td>\n",
       "      <td>0.266514</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            M         F\n",
       "Age                    \n",
       "80   0.061620  0.043899\n",
       "81   0.068153  0.048807\n",
       "82   0.075349  0.054374\n",
       "83   0.083230  0.060661\n",
       "84   0.091933  0.067751\n",
       "85   0.101625  0.075729\n",
       "86   0.112448  0.084673\n",
       "87   0.124502  0.094645\n",
       "88   0.137837  0.105694\n",
       "89   0.152458  0.117853\n",
       "90   0.168352  0.131146\n",
       "91   0.185486  0.145585\n",
       "92   0.203817  0.161175\n",
       "93   0.223298  0.177910\n",
       "94   0.243867  0.195774\n",
       "95   0.264277  0.213849\n",
       "96   0.284168  0.231865\n",
       "97   0.303164  0.249525\n",
       "98   0.320876  0.266514"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "full_life_table = pd.read_csv('../data/life_table.csv')\n",
    "full_life_table.set_index('Age',inplace=True)\n",
    "\n",
    "full_life_table[80:99]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# grab the values for the \"Male\" column\n",
    "prob_death = full_life_table.M.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It would be slightly more convient to work with these values if we knew, for a man of any particular age, the probability of being alive at any age. We calculate a new life table which has along each row $x$ the probability that a man of age $x$ will live to reach age $y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Create a new life table\n",
    "l = len(prob_death)\n",
    "life_table = np.ones((l,l))\n",
    "for i in range(0,l,1):\n",
    "    for j in range(i,l,1):\n",
    "        life_table[i][j]=np.prod(1 - prob_death[i:j+1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
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       "  that the widgets JavaScript is still loading. If this message persists, it\n",
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       "QgridWidget(grid_options={'fullWidthRows': True, 'syncColumnCellResize': True, 'forceFitColumns': True, 'defaultColumnWidth': 150, 'rowHeight': 28, 'enableColumnReorder': False, 'enableTextSelectionOnCells': True, 'editable': True, 'autoEdit': False, 'explicitInitialization': True, 'maxVisibleRows': 15, 'minVisibleRows': 8}, precision=5, show_toolbar=True)"
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     "metadata": {},
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   ],
   "source": [
    "# Load current apostle ages and seniority\n",
    "apostle_data = pd.read_csv('../data/apostles.csv', parse_dates=['Birth', 'Twelve', 'Ordained'])\n",
    "now = pd.Timestamp(datetime.now())\n",
    "apostle_data['Current Age'] = (now - apostle_data['Birth']).astype('<m8[Y]')\n",
    "ad = qg.QGridWidget(df=apostle_data, show_toolbar=True)\n",
    "ad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Helper class\n",
    "\n",
    "For programming convenience, this class captures some simple calculations we will need to do for each prophet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Apostle:\n",
    "    def __init__(self,name,birth,twelve,ordained,seniority):\n",
    "        self.name=name\n",
    "        self.birth=birth\n",
    "        self.twelve=twelve\n",
    "        self.ordained=ordained\n",
    "        self.seniority=seniority\n",
    "    \n",
    "    def __str__(self):\n",
    "        return self.name\n",
    "    \n",
    "    def age(self,year):\n",
    "        \"\"\"Return the apostle's age in a particular year.\"\"\"\n",
    "        return year-self.birth.year\n",
    "    \n",
    "    def current_age(self):\n",
    "        \"\"\"Return the apostle's age in the current year.\"\"\"\n",
    "        current_year = datetime.now().year\n",
    "        return self.age(current_year)\n",
    "    \n",
    "    def most_probable_death_year(self,life_table):\n",
    "        \"\"\"Return the apostle's most likely year of death given\n",
    "        a particular life table.\"\"\"\n",
    "        current_age = self.current_age()\n",
    "        age_of_death = np.argmax(life_table[current_age]<.5)\n",
    "        return self.birth.year + age_of_death\n",
    "    \n",
    "    def most_probable_life_state(self,year,life_table):\n",
    "        \"\"\"Return True if, given the most probable year of death,\n",
    "        the apostle is alive in any part of a particular year\n",
    "        given a particular life table.\"\"\"\n",
    "        return year <= self.most_probable_death_year(life_table)\n",
    "    \n",
    "    def simulate_death_year(self,life_table):\n",
    "        \"\"\"Return a death year randomly drawn from the distribution\n",
    "        of likely death years given a particular life table.\"\"\"\n",
    "        death_year = np.argmin(life_table[self.current_age()] > np.random.random(len(life_table[0])))\n",
    "        return self.birth.year + death_year\n",
    "    \n",
    "    def simulate_life_state(self,year,life_table):\n",
    "        \"\"\"Return True if the apostle is alive given a year of death\n",
    "        drawn from the distribution of likely death years given\n",
    "        by a particular life table.\"\"\"\n",
    "        life_state = self.simulate_death_year(life_table)\n",
    "        return year <= self.simulate_death_year(life_table)\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "    1. Russell M. Nelson is 94 years old.\n",
      "    Life table predicts he will live to age 96.\n",
      "\n",
      "    2. Dallin H. Oaks is 86 years old.\n",
      "    Life table predicts he will live to age 90.\n",
      "\n",
      "    2. M. Russell Ballard is 90 years old.\n",
      "    Life table predicts he will live to age 93.\n",
      "\n",
      "    5. Jeffrey R. Holland is 78 years old.\n",
      "    Life table predicts he will live to age 86.\n",
      "\n",
      "    6. Henry B. Eyring is 85 years old.\n",
      "    Life table predicts he will live to age 90.\n",
      "\n",
      "    7. Dieter F. Uchtdorf is 78 years old.\n",
      "    Life table predicts he will live to age 86.\n",
      "\n",
      "    8. David A. Bednar is 66 years old.\n",
      "    Life table predicts he will live to age 83.\n",
      "\n",
      "    9. Quentin L. Cook is 78 years old.\n",
      "    Life table predicts he will live to age 86.\n",
      "\n",
      "    10. D. Todd Christofferson is 73 years old.\n",
      "    Life table predicts he will live to age 84.\n",
      "\n",
      "    11. Neil L. Andersen is 67 years old.\n",
      "    Life table predicts he will live to age 83.\n",
      "\n",
      "    12. Ronald A. Rasband is 67 years old.\n",
      "    Life table predicts he will live to age 83.\n",
      "\n",
      "    13. Gary E. Stevenson is 63 years old.\n",
      "    Life table predicts he will live to age 82.\n",
      "\n",
      "    14. Dale G. Renlund is 66 years old.\n",
      "    Life table predicts he will live to age 83.\n"
     ]
    }
   ],
   "source": [
    "# Create apostle objects and print their ages\n",
    "apostles = []\n",
    "for i,row in apostle_data.iterrows():\n",
    "    apostle = Apostle(row.Name,row.Birth,row.Twelve,row.Ordained,row.Seniority)\n",
    "    apostles.append(apostle)\n",
    "    dy = apostle.most_probable_death_year(life_table)\n",
    "    age_death = dy - apostle.birth.year\n",
    "    msg = \"\"\"\n",
    "    {}. {} is {} years old.\n",
    "    Life table predicts he will live to age {}.\"\"\"\n",
    "    print(msg.format(apostle.seniority,apostle.name,apostle.current_age(),age_death))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Methodology\n",
    "Now we define two more functions to help us calculate who is prophet in a particular year.\n",
    "Each of these functions uses a different method to calculate who will be prophet:\n",
    "\n",
    "#### Method 1: Winner takes all\n",
    "The simplest method simply calculates which year each apostle is likely to die in (by\n",
    "taking the first year they are more likely to be dead than alive) and returns the most\n",
    "senior living apostle who is more likely to be alive than dead.\n",
    "\n",
    "#### Method 2: Monte-Carlo simulation\n",
    "A slightly more interesting (and more robust) method runs a simulation for each apostle,\n",
    "making draws from the whole distribution of probable years of death. If we run this\n",
    "simulation many many times, we will end up with estimates of the probability that each\n",
    "apostle will be prophet in any particular year. This method will end up giving us a\n",
    "clearer picture than the winner takes all method.\n",
    "\n",
    "#### Method 3: Accounting for health\n",
    "This method repeats the Monte-Carlo simulation but allows for manual adjustment of the health of\n",
    "the apostles be adding or subtracting years from their life. By default, since all have lived very healthy\n",
    "lives, eight years are subtracted from each of their ages (to simulate an average life expectancy of 85. From there, up to two years is added or subtracted to account for perceived health status (very unhealthy, unhealty, normal, healthy, very healthy)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define some helper functions for calculating who is prophet in a particular year\n",
    "# using two different methods\n",
    "\n",
    "def most_probable_prophet_in_year(apostles,year,life_table):\n",
    "    \"\"\"Return the apostle (given a list of apostles) most likely\n",
    "    to be prophet in a particular year\"\"\"\n",
    "    apostles_alive = [apostle for apostle in apostles\n",
    "                      if apostle.most_probable_life_state(year,life_table)]\n",
    "    \n",
    "    if len(apostles_alive) == 0:\n",
    "        return None\n",
    "    \n",
    "    apostle_index = np.argmin([apostle.seniority for apostle in apostles_alive])\n",
    "    return apostles_alive[apostle_index]\n",
    "\n",
    "def simulate_prophet_in_year(apostles,year,life_table):\n",
    "    \"\"\"Return the apostle (given a list of apostles) who is prophet\n",
    "    in a particular year after simulating each apostle's life state\n",
    "    in the given year.\"\"\"\n",
    "    apostles_alive = [apostle for apostle in apostles\n",
    "                      if apostle.simulate_life_state(year,life_table)]\n",
    "    if len(apostles_alive) == 0:\n",
    "        return None\n",
    "    \n",
    "    apostle_index = np.argmin([apostle.seniority for apostle in apostles_alive])\n",
    "    return apostles_alive[apostle_index]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ICHh7e6OsrAxeXl4YP358pRnhOXPmYNmyZfjyyy+h1Wrh7u6OIUOGwNHR8Z71gKgx0Ajnb4ksori4GOvXr8err76K1q1bIzc3F4GBgdi7d2+1s2ONgaIoCA8PR5cuXfDyyy+rXQ4R0QOBM2NEFmJra4sWLVrA19cXOp0OOp3OPIPRGBUXF8PNzQ1OTk53NItCRER3hjNjRERERCriG/iJiIiIVMQwRkRERKQihjEiIiIiFTW6N/BfuFCkdglNQrt2bXDp0jW1yyALYo+bP/a4eWN/m7927dpAp9Pe9X44M9ZE3YvmU+PGHjd/7HHzxv42f/eqxwxjRERERCpiGCMiIiJSEcMYERERkYoa3Rv4m4uA2DSL7v+bNT4W3T8RERHdH5wZIyIiIlIRwxgRERGRihjGiIiIiFTEMEZERESkIoYxIiIiIhUxjBERERGpiGGMiIiISEV1fs+YyWRCaGgoTp48Ca1Wi5iYGIgI9Ho9NBoNevXqhRUrVsDKygoJCQnYvXs3dDodQkJC4OjoiNOnT1c7loiIiIjqMTP2ww8/AAA2btyI+fPnIyYmBjExMQgKCkJycjJEBKmpqcjNzUVOTg42bdqE+Ph4rFq1CgCqHUtEREREN9QZxtzd3REREQEAyM/PR8eOHZGbm4uhQ4cCAFxdXZGZmYn9+/dj1KhR0Gg06NKlC0wmEwoLC6sdS0REREQ31OvnkHQ6HYKDg7Fr1y68/fbb+OGHH6DRaAAANjY2KCoqQnFxMezt7c3bVCwXkSpja9OuXRvodNo7PZ8HSqdOdmqXQBbGHjd/7HHzxv5SfdT7tylXr16NxYsXY8qUKSgtLTUvNxgMaNu2LWxtbWEwGCott7Ozq/T+sIqxtbl06VpD6n+gXbhQe7Clpq1TJzv2uJljj5s39rf5u1dhu87HlF9//TUSExMBAK1bt4ZGo8GAAQOQnZ0NAEhPT4ezszOcnJyQkZEBRVGQn58PRVHQvn179O/fv8pYIiIiIrqhzpmxZ555BkuXLsX06dNRXl6OkJAQ9OjRA2FhYYiPj4eDgwM8PDyg1Wrh7OyMqVOnQlEULF++HAAQHBxcZSwRERER3aAREVG7iFs1lyndgNg0i+7/mzU+zeZaUfX4iKP5Y4+bN/a3+btvjymJiIiIyHIYxoiIiIhUxDBGREREpCKGMSIiIiIVMYwRERERqYhhjIiIiEhFDGNEREREKmIYIyIiIlIRwxgRERGRihjGiIiIiFRU529TUuPkvejfFt3/R/oxFt0/ERER3cCZMSIiIiIVMYwRERERqeiBfUwZEJumdglEREREnBkjIiIiUhPDGBEREZGKGMaIiIiIVMQwRkRERKQihjEiIiIiFTGMEREREamIYYyIiIhIRQxjRERERCpiGCMiIiJSUa3fwG80GhESEoJz586hrKwMs2fPRs+ePaHX66HRaNCrVy+sWLECVlZWSEhIwO7du6HT6RASEgJHR0ecPn262rFEREREdEOtyWjr1q2wt7dHcnIyPvjgA0RERCAmJgZBQUFITk6GiCA1NRW5ubnIycnBpk2bEB8fj1WrVgFAtWOJiIiI6KZaw9jYsWOxYMEC82utVovc3FwMHToUAODq6orMzEzs378fo0aNgkajQZcuXWAymVBYWFjtWCIiIiK6qdbHlDY2NgCA4uJizJ8/H0FBQVi9ejU0Go15fVFREYqLi2Fvb19pu6KiIohIlbF1adeuDXQ67R2fEN0bnTrZqV0CgX14ELDHzRv7S/VRaxgDgIKCAsydOxfTpk2Dt7c33nzzTfM6g8GAtm3bwtbWFgaDodJyOzu7Su8Pqxhbl0uXrjX0HMgCLlyoOziTZXXqZMc+NHPscfPG/jZ/9yps1/qY8uLFiwgICMCSJUvg6+sLAOjfvz+ys7MBAOnp6XB2doaTkxMyMjKgKAry8/OhKArat29f7VgiIiIiuqnWmbH3338fV69exfr167F+/XoAwLJlyxAZGYn4+Hg4ODjAw8MDWq0Wzs7OmDp1KhRFwfLlywEAwcHBCAsLqzSWiIiIiG7SiIioXcSt7teUbkBs2n05TlP1kX6M2iU88PiIo/ljj5s39rf5uy+PKYmIiIjIshjGiIiIiFTEMEZERESkIoYxIiIiIhUxjBERERGpiGGMiIiISEUMY0REREQqYhgjIiIiUhHDGBEREZGKGMaIiIiIVMQwRkRERKQihjEiIiIiFTGMEREREamIYYyIiIhIRQxjRERERCpiGCMiIiJSEcMYERERkYoYxoiIiIhUxDBGREREpCKd2gVQ4xQQm2bR/X+kH2PR/RMRETUVnBkjIiIiUhHDGBEREZGKGMaIiIiIVFSvMPbrr7/C398fAHD69Gk8//zzmDZtGlasWAFFUQAACQkJ8PX1hZ+fHw4dOlTrWCIiIiK6oc4w9sEHHyA0NBSlpaUAgJiYGAQFBSE5ORkigtTUVOTm5iInJwebNm1CfHw8Vq1aVeNYIiIiIrqpzjD26KOP4p133jG/zs3NxdChQwEArq6uyMzMxP79+zFq1ChoNBp06dIFJpMJhYWF1Y4lIiIiopvq/GoLDw8PnD171vxaRKDRaAAANjY2KCoqQnFxMezt7c1jKpZXN7Yu7dq1gU6nbfCJUNPSqZOd2iU0CbxOzR973Lyxv1QfDf6eMSurm5NpBoMBbdu2ha2tLQwGQ6XldnZ21Y6ty6VL1xpaEjVBFy7UHcwfdJ062fE6NXPscfPG/jZ/9ypsN/jTlP3790d2djYAID09Hc7OznByckJGRgYURUF+fj4URUH79u2rHUtERERENzV4Ziw4OBhhYWGIj4+Hg4MDPDw8oNVq4ezsjKlTp0JRFCxfvrzGsURERER0k0ZERO0ibnW/pnQt/XM/VDv+HFLd+Iij+WOPmzf2t/lT7TElEREREd07DGNEREREKmIYIyIiIlIRwxgRERGRihjGiIiIiFTEMEZERESkIoYxIiIiIhUxjBERERGpiGGMiIiISEUMY0REREQqYhgjIiIiUhHDGBEREZGKGMaIiIiIVMQwRkRERKQindoF0IMpIDbNovv/SD/GovsnIiK6VzgzRkRERKQihjEiIiIiFTGMEREREamIYYyIiIhIRQxjRERERCpiGCMiIiJSEcMYERERkYos/j1jiqJg5cqVOH78OFq2bInIyEh069bN0oclIiIiahIsPjP2/fffo6ysDF9++SUWLVqE2NhYSx+SiIiIqMmw+MzY/v374eLiAgAYOHAgjhw5YulDEln8G/4Bfss/ERHdGxafGSsuLoatra35tVarRXl5uaUPS0RERNQkWHxmzNbWFgaDwfxaURTodDUftlMnO0uXBAD4Zo3PfTkO0d24X/cDqYc9bt7YX6oPi8+MOTk5IT09HQBw8OBB9O7d29KHJCIiImoyNCIiljxAxacpT5w4ARFBdHQ0evToYclDEhERETUZFg9jRERERFQzfukrERERkYoYxoiIiIhUxDBGREREpCKLf7UF1Z/RaERISAjOnTuHsrIyzJ49Gz179oRer4dGo0GvXr2wYsUKWFlZYfXq1Thw4ADKy8sxdepUTJkyBYWFhVi8eDFKSkrQuXNnxMTEoHXr1mqfFt3ibnt8+fJleHh4mD+V7O7ujpkzZ6p8VnSrhvT4rbfeQmZmJjQaDUJDQ+Ho6Mj7uAm42x7zPm7cGtJfALh+/Tr8/PywaNEiuLq63tk9LNRobN68WSIjI0VEpLCwUEaPHi2BgYHy448/iohIWFiY7Ny5U7KysmTOnDkiIlJaWiru7u5y+fJliYiIkJSUFBERSUxMlI8//liV86Ca3W2P9+3bJ+Hh4arVT3Wrb49zc3NlxowZoiiK5OXlibe3t4gI7+Mm4G57zPu4catvfyvo9Xrx8fGRPXv2iMid3cN8TNmIjB07FgsWLDC/1mq1yM3NxdChQwEArq6uyMzMxKBBgxAdHW0eZzKZoNPpKv30VMVYalzutsdHjhxBbm4uXnjhBcyfPx/nz5+/7+dAtatvj/v3748NGzZAo9EgPz8fHTt2BADex03A3faY93HjVt/+AsCGDRswaNAg9O3b1zz+Tu5hhrFGxMbGBra2tiguLsb8+fMRFBQEEYFGozGvLyoqgrW1NR566CEYjUbo9XpMnToVNjY2KC4uhp2dXaWx1LjcbY8dHBwwf/58fPbZZ3B3d0dkZKTKZ0S3q2+PAUCn0+Gtt95CYGAgvLy8AID3cRNwtz3mfdy41be/WVlZOH36NKZMmVJp+zu5hxnGGpmCggLMmDEDPj4+8Pb2Nj+TBgCDwYC2bdsCAK5cuYKXXnoJPXr0QGBgIIDKPz1161hqXO6mx8OHD8ewYcMAAE8//TR+++23+38CVKf69hgAXnvtNezduxcbNmzAmTNneB83EXfTY97HjV99+rt582acOHEC/v7+2Lt3L958800cPXr0ju5hhrFG5OLFiwgICMCSJUvg6+sLAOjfvz+ys7MBAOnp6XB2dkZJSQlmzZqF5557DnPnzjVv7+TkhD179pjHDh48+P6fBNXqbnscGhqKHTt2AACysrLw2GOP3f+ToFrVt8dZWVlYtWoVAMDa2ho6nQ4ajYb3cRNwtz3mfdy41be/a9aswcaNG5GUlAQXFxcsWbIE/fr1u6N7mN/A34hERkZi27ZtcHBwMC9btmwZIiMjYTQa4eDggMjISCQlJSEhIQH9+vUzj4uOjkbr1q0RHBwMg8GAdu3aYc2aNWjTpo0ap0I1uNseA0BISAgAoHXr1oiMjETnzp3v70lQrerbYwAIDw/H8ePHoSgKfH19MWXKFFy8eJH3cSN3tz3Oy8vjfdyI1be/Wq3WvF6v12PcuHFwdXW9o3uYYYyIiIhIRXxMSURERKQihjEiIiIiFTGMEREREamIYYyIiIhIRQxjRERERCpiGCMiIiJSEcMYERERkYoYxoiIiIhU9P+f1nW+8KPgiwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bd386d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b8e16d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b8c75f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b7f25c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b5fa748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b9b1630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b8ea550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bba3320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bd165c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bc8bf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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VRfKpfmOOGz/muHFjfhu/usoxizEiIiIiFZlVjH333XcIDg4GAJw8eRLjx4/HhAkTMG/ePNOTt1evXo2AgACMGzfO9G6yqtoSERER0TU1FmN//etfMWfOHJSUlAAAFi1ahJdffhkbN26EiCA5ORnZ2dk4dOgQtmzZguXLl2P+/PlVtiUiIiKi/6vxAv62bdti1apVeO211wAA2dnZ6NevH4Br73lLS0uDq6srPD09odFo8PDDD6OiogL5+fmVth02bJgVu0N094TEpVh1/TuWjbLq+omIqH6osRjz8vLC6dOnTZ9FxPR6F3t7exQUFKCwsBAtWrQwtbn+fWVticg8vjO3W3X9f4sYbNX1ExGRee740RY2Nv8/s2k0GtG8eXM4ODjAaDTe9L2jo2OlbWtSV7eJ3gucnR3VDoEaMB4/9QPz0Lgxv2SOOy7GunXrhoMHD+KJJ55Aamoq3N3d0bZtWyxZsgRTpkzB+fPnoSgKWrZsWWnbmvCZLOZxdnbkM9moVnj8qI/juHFjfhu/uiq277gYCw8PR1RUFJYvX4527drBy8sLWq0Wffv2RVBQEBRFwdy5c6tsS0T1g7WveeNpUCIi82hERNQO4kb8K8I8/ItLfdYuZho6FmM14zhu3Jjfxq+uZsb40FciIiIiFbEYIyIiIlJRvXtROFFd4ClEIiJqKDgzRkRERKQizoyRKjhzRUREdA1nxoiIiIhUxGKMiIiISEUsxoiIiIhUxGKMiIiISEUsxoiIiIhUxGKMiIiISEUsxoiIiIhUxGKMiIiISEUsxoiIiIhUxGKMiIiISEV8HRIRWYW1X3n1t4jBVl0/EdHdwpkxIiIiIhWxGCMiIiJSkUWnKbdt24aPP/4YAFBSUoKjR49i2bJlWLx4MR566CEAwPTp09G3b19ER0fj+PHjsLW1hcFggIuLS91FT0RERNTAWVSM+fn5wc/PDwAwf/58+Pv7Izs7G7Nnz4aXl5ep3Z49e1BaWorNmzcjMzMTcXFxiI+Pr5vIyaqsfb0PERERXVOr05Q//PAD/v3vfyMoKAjZ2dlISkrChAkTEBcXh/Lychw+fBh6vR4A0KtXL2RlZdVJ0ERERESNRa3upkxISEBYWBgAwMPDA0OHDsUjjzyCefPmYdOmTSgsLISDg4OpvVarRXl5OXS6qjfr5NQMOp22NmHdM5ydHdUOgUg1jeX4byz9oMoxv2QOi4uxK1eu4KeffoK7uzsAwN/fH82bNwcADBkyBLt374ajoyOMRqNpGUVRqi3EAODixauWhnRPcXZ2RF5egdphEKmmMRz/HMeNG/Pb+NVVsW3xacqvv/4aTz75JABARDBy5EicP38eAJCRkYHu3bvDzc0NqampAIDMzEx06tSpDkImIiIiajwsnhn7+eef8cgjjwAANBoNDAYDpk2bBjs7O7Rv3x6BgYHQarVIS0vDuHHjICKIjY2ts8CJiIiIGgONiIjaQdyIU7rmsfb0N++mpHvd3XjCP09jNW7Mb+On+mlKIiIiIqo9FmNEREREKmIxRkRERKQiFmNEREREKmIxRkRERKQiFmNEREREKmIxRkRERKQiFmNEREREKmIxRkRERKQiFmNEREREKmIxRkRERKQiFmNEREREKmIxRkRERKQiFmNEREREKtKpHQBZxnfmdrVDIGrUQuJSrL6NHctGWX0bRFT/cWaMiIiISEUsxoiIiIhUZPFpytGjR8PR0REA8MgjjyAoKAgLFy6EVquFp6cnpk2bBkVREB0djePHj8PW1hYGgwEuLi51FjwRERFRQ2dRMVZSUgIASExMNH03atQorFq1Cm3atMHzzz+P7OxsnDlzBqWlpdi8eTMyMzMRFxeH+Pj4uomciIiIqBGwqBg7duwYioqKEBISgvLyckyfPh2lpaVo27YtAMDT0xMZGRnIy8uDXq8HAPTq1QtZWVl1FzkRERFRI2BRMWZnZ4cpU6Zg7NixOHHiBJ577jk0b97c9HN7e3vk5uaisLAQDg4Opu+1Wi3Ky8uh0/EmTiIiIiLAwmLM1dUVLi4u0Gg0cHV1haOjIy5dumT6udFoRPPmzVFcXAyj0Wj6XlGUGgsxJ6dm0Om0loRFRNTgODs7qh0CWRHzS+awqBjbunUrcnJyEB0djV9++QVFRUVo1qwZTp06hTZt2uDAgQOYNm0azp8/jy+//BLe3t7IzMxEp06dalz3xYtXLQmJiKhByssrUDsEshJnZ0fmt5Grq2LbomIsICAAr7/+OsaPHw+NRoPY2FjY2Nhg1qxZqKiogKenJx577DE8+uijSEtLw7hx4yAiiI2NrZOgiYiIiBoLjYiI2kHciH9FmOduPB2ciKxrx7JR/H9eI8aZscavrmbG+NBXIiIiIhWxGCMiIiJSEYsxIiIiIhWxGCMiIiJSEYsxIiIiIhWxGCMiIiJSEd9LRESkEt+Z2626/r9FDLbq+omobnBmjIiIiEhFnBmzEj6UlYiIiMzBmTEiIiIiFbEYIyIiIlIRizEiIiIiFbEYIyIiIlIRizEiIiIiFbEYIyIiIlIRH21BRNRIWfsRO3yoLFHd4MwYERERkYpYjBERERGpyKLTlGVlZYiMjMSZM2dQWlqKqVOn4ne/+x1eeOEF/OEPfwAAjB8/Ht7e3li9ejW++uor6HQ6REZGomfPnnUZPxEREVGDZlEx9umnn6JFixZYsmQJLl68iDFjxiAsLAzPPPMMQkJCTO2ys7Nx6NAhbNmyBefOncP06dORlJRUZ8ETERERNXQWFWPDhw+Hl5eX6bNWq0VWVhZ+/vlnJCcnw8XFBZGRkTh8+DA8PT2h0Wjw8MMPo6KiAvn5+WjZsmWddYCIiIioIbOoGLO3twcAFBYWYsaMGXj55ZdRWlqKsWPHokePHoiPj8c777wDR0dHtGjR4qblCgoKqi3GnJyaQafTWhIWERHdRc7OjmqHUO9xH5E5LH60xblz5xAWFoYJEybA19cXV65cQfPmzQEAw4YNQ0xMDIYMGQKj0Whaxmg0wtGx+gPz4sWrloZERER3UV5egdoh1GvOzo7cR41cXRXbFt1NeeHCBYSEhGD27NkICAgAAEyZMgXff/89ACAjIwPdu3eHm5sbDhw4AEVRcPbsWSiKwlOURERERDewaGZs7dq1uHLlCtasWYM1a9YAACIiIhAbG4smTZqgVatWiImJgYODA/r27YugoCAoioK5c+fWafBEREREDZ1GRETtIG7UWKZ0rf3kayIitfEJ/NXjacrGT9XTlERERERUN/huSiIisgjffUlUN+7ZYoynEYmIiKg+4GlKIiIiIhWxGCMiIiJSEYsxIiIiIhWxGCMiIiJS0T17AT8REdVvvFuT7hWcGSMiIiJSEYsxIiIiIhWxGCMiIiJSEYsxIiIiIhWxGCMiIiJSEYsxIiIiIhWxGCMiIiJSEZ8zRkRE9yRrP8dsx7JRVl0/NR6cGSMiIiJSkdVnxhRFQXR0NI4fPw5bW1sYDAa4uLhYe7NEREREDYLVi7EvvvgCpaWl2Lx5MzIzMxEXF4f4+Hhrb5aIiEhVvjO3W3X9fJ1T42H1Yuzw4cPQ6/UAgF69eiErK8vamyQiImr0rH3NG8CC726xejFWWFgIBwcH02etVovy8nLodLx3gIiIqD7jy9rvDqtXRA4ODjAajabPiqJUW4g5OztaOyQAvMuFiIiI6ger303p5uaG1NRUAEBmZiY6depk7U0SERERNRgaERFrbuD63ZQ5OTkQEcTGxqJ9+/bW3CQRERFRg2H1YoyIiIiIqsaHvhIRERGpiMUYERERkYpYjBERERGpiA/7qkfKysoQGRmJM2fOoLS0FFOnTkWHDh0QEREBjUaDjh07Yt68ebCxscGbb76JI0eOoLy8HEFBQQgMDER+fj5mzZqF4uJitG7dGosWLULTpk3V7hbdoLY5vnTpEry8vEx3JQ8dOhSTJk1SuVd0ozvJ8VtvvYX09HRoNBrMmTMHPXv25DhuAGqbY47j+u1O8gsARUVFGDduHGbOnIkBAwZYNoaF6o2tW7eKwWAQEZH8/HwZOHCghIaGyj//+U8REYmKipI9e/ZIRkaGvPjiiyIiUlJSIkOHDpVLly5JTEyMJCUliYhIQkKCvPfee6r0g6pW2xynpaXJggULVIufamZujrOzs+Xpp58WRVEkNzdXfH19RUQ4jhuA2uaY47h+Mze/10VERMioUaNk3759ImLZGOZpynpk+PDheOmll0yftVotsrOz0a9fPwDAgAEDkJ6ejt69eyM2NtbUrqKiAjqd7qZXT11vS/VLbXOclZWF7OxsTJw4ETNmzMCvv/561/tA1TM3x926dcO6deug0Whw9uxZtGrVCgA4jhuA2uaY47h+Mze/ALBu3Tr07t0bXbp0MbW3ZAyzGKtH7O3t4eDggMLCQsyYMQMvv/wyRAQajcb084KCAtx33324//77UVZWhoiICAQFBcHe3h6FhYVwdHS8qS3VL7XNcbt27TBjxgysX78eQ4cOhcFgULlHdCtzcwwAOp0Ob731FkJDQ+Hj4wMAHMcNQG1zzHFcv5mb34yMDJw8eRKBgYE3LW/JGGYxVs+cO3cOTz/9NEaNGgVfX1/TOWkAMBqNaN68OQDg8uXLePbZZ9G+fXuEhoYCuPnVUze2pfqlNjl2d3fHE088AQAYNmwYfvzxx7vfAaqRuTkGgFdeeQX79+/HunXrcOrUKY7jBqI2OeY4rv/Mye/WrVuRk5OD4OBg7N+/H0uWLMHRo0ctGsMsxuqRCxcuICQkBLNnz0ZAQAAAoFu3bjh48CAAIDU1FX379kVxcTEmT54Mf39/hIWFmZZ3c3PDvn37TG379Olz9ztB1aptjufMmYPdu3cDADIyMtC9e/e73wmqlrk5zsjIwPz58wEA9913H3Q6HTQaDcdxA1DbHHMc12/m5nfZsmXYtGkTEhMTodfrMXv2bHTt2tWiMcwn8NcjBoMBu3btQrt27UzfvfHGGzAYDCgrK0O7du1gMBiQmJiI1atXo2vXrqZ2sbGxaNq0KcLDw2E0GuHk5IRly5ahWbNmanSFqlDbHANAZGQkAKBp06YwGAxo3br13e0EVcvcHAPAggULcPz4cSiKgoCAAAQGBuLChQscx/VcbXOcm5vLcVyPmZtfrVZr+nlERAS8vb0xYMAAi8YwizEiIiIiFfE0JREREZGKWIwRERERqYjFGBEREZGKWIwRERERqYjFGBEREZGKWIwRERERqYjFGBEREZGKWIwRERERqei/Pd7+LUs8jwoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bca4a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bc87470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1101e74e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot a histogram of each apostle's likely death years\n",
    "for apostle in apostles:\n",
    "    death_year_dist = []\n",
    "    for i in range(10000):\n",
    "        death_year_dist.append(apostle.simulate_death_year(life_table))\n",
    "\n",
    "    plt.hist(death_year_dist,bins=range(CURRENT_YEAR,2040))\n",
    "    plt.title(\"Histogram of year of death of {}\".format(apostle.name))\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Russell M. Nelson\n"
     ]
    }
   ],
   "source": [
    "# Given our model, who is most likely to be prophet in the year 2020?\n",
    "print(most_probable_prophet_in_year(apostles,2020,life_table))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2018: Russell M. Nelson\n",
      "2019: Russell M. Nelson\n",
      "2020: Russell M. Nelson\n",
      "2021: Dallin H. Oaks\n",
      "2022: Dallin H. Oaks\n",
      "2023: Jeffrey R. Holland\n",
      "2024: Jeffrey R. Holland\n",
      "2025: Jeffrey R. Holland\n",
      "2026: Jeffrey R. Holland\n",
      "2027: David A. Bednar\n",
      "2028: David A. Bednar\n",
      "2029: David A. Bednar\n",
      "2030: David A. Bednar\n",
      "2031: David A. Bednar\n",
      "2032: David A. Bednar\n",
      "2033: David A. Bednar\n",
      "2034: David A. Bednar\n",
      "2035: David A. Bednar\n",
      "2036: Gary E. Stevenson\n",
      "2037: Gary E. Stevenson\n",
      "2038: None\n",
      "2039: None\n",
      "2040: None\n",
      "2041: None\n",
      "2042: None\n"
     ]
    }
   ],
   "source": [
    "# Given our model, who is most likely to be prophet in every year from now until 2040?\n",
    "for year in range(CURRENT_YEAR,CURRENT_YEAR+25):\n",
    "    print(\"{}: {}\".format(year, most_probable_prophet_in_year(apostles,year,life_table)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 2 - simulation:\n",
    "\n",
    "What if we looked at the probabilities over 10000 trials? This would give us a\n",
    "more accurate picture of how likely it is that any of the current apostles\n",
    "will be prophet in any particular year. Note that it is possible (and probable)\n",
    "that in some of the later years none of the current apostles will be alive. In\n",
    "these cases, I have assigned a probability of prophethood to \"other\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_simulation(n_trials,apostles,life_table):\n",
    "    for year in range(CURRENT_YEAR,CURRENT_YEAR+25):\n",
    "        prophets = defaultdict(list)\n",
    "        for i in range(n_trials):\n",
    "            prophet = simulate_prophet_in_year(apostles,year,life_table)\n",
    "            if prophet is not None:\n",
    "                prophets[prophet.name].append(1)\n",
    "            else:\n",
    "                prophets[\"other\"].append(1)\n",
    "        probabilities = []\n",
    "        for key,count in prophets.items():\n",
    "            probabilities.append((key,float(len(count))/n_trials))\n",
    "        probabilities = sorted(probabilities,key=lambda x: x[1],reverse=True)\n",
    "        print(year)\n",
    "        for name,probability in probabilities:\n",
    "            print(\" {} ({})\\n\".format(name,probability))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2018\n",
      " Russell M. Nelson (1.0)\n",
      "\n",
      "2019\n",
      " Russell M. Nelson (0.7563)\n",
      "\n",
      " Dallin H. Oaks (0.2166)\n",
      "\n",
      " M. Russell Ballard (0.0219)\n",
      "\n",
      " Jeffrey R. Holland (0.005)\n",
      "\n",
      " Henry B. Eyring (0.0002)\n",
      "\n",
      "2020\n",
      " Russell M. Nelson (0.4194)\n",
      "\n",
      " Dallin H. Oaks (0.4024)\n",
      "\n",
      " M. Russell Ballard (0.104)\n",
      "\n",
      " Jeffrey R. Holland (0.064)\n",
      "\n",
      " Henry B. Eyring (0.0082)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0018)\n",
      "\n",
      " David A. Bednar (0.0002)\n",
      "\n",
      "2021\n",
      " Dallin H. Oaks (0.389)\n",
      "\n",
      " Jeffrey R. Holland (0.2171)\n",
      "\n",
      " Russell M. Nelson (0.1671)\n",
      "\n",
      " M. Russell Ballard (0.136)\n",
      "\n",
      " Henry B. Eyring (0.0478)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0306)\n",
      "\n",
      " David A. Bednar (0.0108)\n",
      "\n",
      " D. Todd Christofferson (0.0008)\n",
      "\n",
      " Quentin L. Cook (0.0008)\n",
      "\n",
      "2022\n",
      " Jeffrey R. Holland (0.3361)\n",
      "\n",
      " Dallin H. Oaks (0.2523)\n",
      "\n",
      " Dieter F. Uchtdorf (0.1123)\n",
      "\n",
      " Henry B. Eyring (0.0851)\n",
      "\n",
      " M. Russell Ballard (0.0849)\n",
      "\n",
      " David A. Bednar (0.0662)\n",
      "\n",
      " Russell M. Nelson (0.0484)\n",
      "\n",
      " Quentin L. Cook (0.0089)\n",
      "\n",
      " D. Todd Christofferson (0.0041)\n",
      "\n",
      " Neil L. Andersen (0.0015)\n",
      "\n",
      " Ronald A. Rasband (0.0002)\n",
      "\n",
      "2023\n",
      " Jeffrey R. Holland (0.3372)\n",
      "\n",
      " David A. Bednar (0.186)\n",
      "\n",
      " Dieter F. Uchtdorf (0.1702)\n",
      "\n",
      " Dallin H. Oaks (0.1205)\n",
      "\n",
      " Henry B. Eyring (0.0772)\n",
      "\n",
      " M. Russell Ballard (0.0369)\n",
      "\n",
      " Quentin L. Cook (0.0248)\n",
      "\n",
      " D. Todd Christofferson (0.0206)\n",
      "\n",
      " Neil L. Andersen (0.013)\n",
      "\n",
      " Russell M. Nelson (0.0099)\n",
      "\n",
      " Ronald A. Rasband (0.0024)\n",
      "\n",
      " Gary E. Stevenson (0.001)\n",
      "\n",
      " Dale G. Renlund (0.0003)\n",
      "\n",
      "2024\n",
      " David A. Bednar (0.305)\n",
      "\n",
      " Jeffrey R. Holland (0.2506)\n",
      "\n",
      " Dieter F. Uchtdorf (0.1688)\n",
      "\n",
      " D. Todd Christofferson (0.0506)\n",
      "\n",
      " Quentin L. Cook (0.0492)\n",
      "\n",
      " Dallin H. Oaks (0.0474)\n",
      "\n",
      " Henry B. Eyring (0.0456)\n",
      "\n",
      " Neil L. Andersen (0.0449)\n",
      "\n",
      " Ronald A. Rasband (0.0184)\n",
      "\n",
      " M. Russell Ballard (0.0086)\n",
      "\n",
      " Gary E. Stevenson (0.0077)\n",
      "\n",
      " Dale G. Renlund (0.0016)\n",
      "\n",
      " Russell M. Nelson (0.0009)\n",
      "\n",
      " other (0.0007)\n",
      "\n",
      "2025\n",
      " David A. Bednar (0.3793)\n",
      "\n",
      " Jeffrey R. Holland (0.1541)\n",
      "\n",
      " Dieter F. Uchtdorf (0.129)\n",
      "\n",
      " D. Todd Christofferson (0.0867)\n",
      "\n",
      " Neil L. Andersen (0.0863)\n",
      "\n",
      " Quentin L. Cook (0.0499)\n",
      "\n",
      " Ronald A. Rasband (0.0406)\n",
      "\n",
      " Gary E. Stevenson (0.0252)\n",
      "\n",
      " Henry B. Eyring (0.0178)\n",
      "\n",
      " Dallin H. Oaks (0.0149)\n",
      "\n",
      " Dale G. Renlund (0.0081)\n",
      "\n",
      " other (0.0065)\n",
      "\n",
      " M. Russell Ballard (0.0015)\n",
      "\n",
      " Russell M. Nelson (0.0001)\n",
      "\n",
      "2026\n",
      " David A. Bednar (0.3777)\n",
      "\n",
      " Neil L. Andersen (0.1329)\n",
      "\n",
      " D. Todd Christofferson (0.0943)\n",
      "\n",
      " Jeffrey R. Holland (0.0876)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0756)\n",
      "\n",
      " Ronald A. Rasband (0.0737)\n",
      "\n",
      " Gary E. Stevenson (0.0608)\n",
      "\n",
      " Quentin L. Cook (0.0396)\n",
      "\n",
      " other (0.0236)\n",
      "\n",
      " Dale G. Renlund (0.0222)\n",
      "\n",
      " Henry B. Eyring (0.0078)\n",
      "\n",
      " Dallin H. Oaks (0.0041)\n",
      "\n",
      " M. Russell Ballard (0.0001)\n",
      "\n",
      "2027\n",
      " David A. Bednar (0.3348)\n",
      "\n",
      " Neil L. Andersen (0.1558)\n",
      "\n",
      " Ronald A. Rasband (0.1025)\n",
      "\n",
      " Gary E. Stevenson (0.0954)\n",
      "\n",
      " D. Todd Christofferson (0.0862)\n",
      "\n",
      " other (0.0737)\n",
      "\n",
      " Jeffrey R. Holland (0.0425)\n",
      "\n",
      " Dale G. Renlund (0.0424)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0401)\n",
      "\n",
      " Quentin L. Cook (0.0249)\n",
      "\n",
      " Henry B. Eyring (0.0015)\n",
      "\n",
      " Dallin H. Oaks (0.0002)\n",
      "\n",
      "2028\n",
      " David A. Bednar (0.2608)\n",
      "\n",
      " other (0.1642)\n",
      "\n",
      " Neil L. Andersen (0.1505)\n",
      "\n",
      " Gary E. Stevenson (0.1279)\n",
      "\n",
      " Ronald A. Rasband (0.1166)\n",
      "\n",
      " Dale G. Renlund (0.0658)\n",
      "\n",
      " D. Todd Christofferson (0.0601)\n",
      "\n",
      " Jeffrey R. Holland (0.0201)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0194)\n",
      "\n",
      " Quentin L. Cook (0.0142)\n",
      "\n",
      " Henry B. Eyring (0.0004)\n",
      "\n",
      "2029\n",
      " other (0.2867)\n",
      "\n",
      " David A. Bednar (0.1988)\n",
      "\n",
      " Gary E. Stevenson (0.1526)\n",
      "\n",
      " Neil L. Andersen (0.1304)\n",
      "\n",
      " Ronald A. Rasband (0.1078)\n",
      "\n",
      " Dale G. Renlund (0.0698)\n",
      "\n",
      " D. Todd Christofferson (0.0355)\n",
      "\n",
      " Jeffrey R. Holland (0.007)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0057)\n",
      "\n",
      " Quentin L. Cook (0.0055)\n",
      "\n",
      " Henry B. Eyring (0.0002)\n",
      "\n",
      "2030\n",
      " other (0.4378)\n",
      "\n",
      " David A. Bednar (0.1456)\n",
      "\n",
      " Gary E. Stevenson (0.1398)\n",
      "\n",
      " Neil L. Andersen (0.0969)\n",
      "\n",
      " Ronald A. Rasband (0.086)\n",
      "\n",
      " Dale G. Renlund (0.0683)\n",
      "\n",
      " D. Todd Christofferson (0.0203)\n",
      "\n",
      " Quentin L. Cook (0.0021)\n",
      "\n",
      " Jeffrey R. Holland (0.0018)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0014)\n",
      "\n",
      "2031\n",
      " other (0.5868)\n",
      "\n",
      " Gary E. Stevenson (0.1268)\n",
      "\n",
      " David A. Bednar (0.0931)\n",
      "\n",
      " Neil L. Andersen (0.0649)\n",
      "\n",
      " Ronald A. Rasband (0.0591)\n",
      "\n",
      " Dale G. Renlund (0.0582)\n",
      "\n",
      " D. Todd Christofferson (0.01)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0007)\n",
      "\n",
      " Quentin L. Cook (0.0004)\n",
      "\n",
      "2032\n",
      " other (0.7185)\n",
      "\n",
      " Gary E. Stevenson (0.0953)\n",
      "\n",
      " David A. Bednar (0.0554)\n",
      "\n",
      " Dale G. Renlund (0.0451)\n",
      "\n",
      " Neil L. Andersen (0.0417)\n",
      "\n",
      " Ronald A. Rasband (0.0404)\n",
      "\n",
      " D. Todd Christofferson (0.0033)\n",
      "\n",
      " Jeffrey R. Holland (0.0002)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0001)\n",
      "\n",
      "2033\n",
      " other (0.8178)\n",
      "\n",
      " Gary E. Stevenson (0.0694)\n",
      "\n",
      " David A. Bednar (0.0386)\n",
      "\n",
      " Dale G. Renlund (0.0287)\n",
      "\n",
      " Neil L. Andersen (0.0248)\n",
      "\n",
      " Ronald A. Rasband (0.019)\n",
      "\n",
      " D. Todd Christofferson (0.0016)\n",
      "\n",
      " Quentin L. Cook (0.0001)\n",
      "\n",
      "2034\n",
      " other (0.8896)\n",
      "\n",
      " Gary E. Stevenson (0.0475)\n",
      "\n",
      " David A. Bednar (0.0198)\n",
      "\n",
      " Dale G. Renlund (0.0175)\n",
      "\n",
      " Ronald A. Rasband (0.0124)\n",
      "\n",
      " Neil L. Andersen (0.0123)\n",
      "\n",
      " D. Todd Christofferson (0.0009)\n",
      "\n",
      "2035\n",
      " other (0.9389)\n",
      "\n",
      " Gary E. Stevenson (0.029)\n",
      "\n",
      " David A. Bednar (0.0086)\n",
      "\n",
      " Dale G. Renlund (0.0086)\n",
      "\n",
      " Neil L. Andersen (0.0082)\n",
      "\n",
      " Ronald A. Rasband (0.0065)\n",
      "\n",
      " D. Todd Christofferson (0.0002)\n",
      "\n",
      "2036\n",
      " other (0.968)\n",
      "\n",
      " Gary E. Stevenson (0.0171)\n",
      "\n",
      " David A. Bednar (0.0053)\n",
      "\n",
      " Dale G. Renlund (0.0049)\n",
      "\n",
      " Neil L. Andersen (0.0026)\n",
      "\n",
      " Ronald A. Rasband (0.0021)\n",
      "\n",
      "2037\n",
      " other (0.9883)\n",
      "\n",
      " Gary E. Stevenson (0.0072)\n",
      "\n",
      " David A. Bednar (0.0018)\n",
      "\n",
      " Dale G. Renlund (0.0014)\n",
      "\n",
      " Neil L. Andersen (0.0011)\n",
      "\n",
      " Ronald A. Rasband (0.0002)\n",
      "\n",
      "2038\n",
      " other (0.9941)\n",
      "\n",
      " Gary E. Stevenson (0.0035)\n",
      "\n",
      " David A. Bednar (0.0011)\n",
      "\n",
      " Dale G. Renlund (0.0009)\n",
      "\n",
      " Neil L. Andersen (0.0003)\n",
      "\n",
      " Ronald A. Rasband (0.0001)\n",
      "\n",
      "2039\n",
      " other (0.9969)\n",
      "\n",
      " Gary E. Stevenson (0.0025)\n",
      "\n",
      " Dale G. Renlund (0.0003)\n",
      "\n",
      " Neil L. Andersen (0.0002)\n",
      "\n",
      " David A. Bednar (0.0001)\n",
      "\n",
      "2040\n",
      " other (0.9983)\n",
      "\n",
      " Gary E. Stevenson (0.0017)\n",
      "\n",
      "2041\n",
      " other (0.9996)\n",
      "\n",
      " Gary E. Stevenson (0.0004)\n",
      "\n",
      "2042\n",
      " other (1.0)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "run_simulation(10000,apostles,life_table)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Method 2  - conclusions\n",
    "\n",
    "Interestingly, for many of the years far down the line, the apostle most likely to be prophet is far from clear.\n",
    "\n",
    "By 2029 our model says that it is more likely that someone other than one of the current apostles will be prophet. However, since our model systematically underestimates the age of death of these men, we should take this number with a grain of salt. In 25 years there is virtually no possiblity that anyone of the apostles will be living. it's extraordinarily unlikely that any of the current apostles will still be alive. Gary E. Stevenson is the youngest apostle living and our model only predicts a .01% chance of living that long.\n",
    "\n",
    "#### Caveats\n",
    "This model did not explicitly take health state into account, but approximated it using current age. Method 3 is one way of accounting for this.\n",
    "\n",
    "### Method 3 - adjusting for health and systematic mortality biases.\n",
    "One way to approximate of actual health status is to adjust their ages to reflect both their current health and the greater-than-average overall health of their demographic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "default = 5\n",
    "apostle_age_adjustments = {\n",
    "    # All defaults - church has done a solid job limiting news of apostles health\n",
    "    \"Russell M. Nelson\":  default,\n",
    "    \"Dallin H. Oaks\":     default,\n",
    "    \"M. Russell Ballard\": default,\n",
    "    \"Jeffrey R. Holland\": default,\n",
    "    \"Henry B. Eyring\":    default,\n",
    "    \"Dieter F. Uchtdorf\": default,\n",
    "    \"David A. Bednar\":    default,\n",
    "    \"Quentin L. Cook\":    default,\n",
    "    \"D. Todd Christofferson\": default,\n",
    "    \"Neil L. Andersen\":   default,\n",
    "    \"Ronald A. Rasband\": default,\n",
    "    \"Gary E. Stevenson\": default,\n",
    "    \"Dale G. Renlund\": default,\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "adj_apostles = []\n",
    "for apostle in apostles:\n",
    "    adg_adj = apostle_age_adjustments[apostle.name]\n",
    "    adj_apostles.append(Apostle(\n",
    "        apostle.name,\n",
    "        (a.birth + timedelta(days=8*365)),\n",
    "        apostle.twelve,\n",
    "        apostle.ordained,\n",
    "        apostle.seniority))     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2018\n",
      " Russell M. Nelson (1.0)\n",
      "\n",
      "2019\n",
      " Russell M. Nelson (0.8898)\n",
      "\n",
      " Dallin H. Oaks (0.0988)\n",
      "\n",
      " M. Russell Ballard (0.0104)\n",
      "\n",
      " Jeffrey R. Holland (0.0009)\n",
      "\n",
      " Henry B. Eyring (0.0001)\n",
      "\n",
      "2020\n",
      " Russell M. Nelson (0.6929)\n",
      "\n",
      " Dallin H. Oaks (0.2106)\n",
      "\n",
      " M. Russell Ballard (0.0678)\n",
      "\n",
      " Jeffrey R. Holland (0.0202)\n",
      "\n",
      " Henry B. Eyring (0.0057)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0019)\n",
      "\n",
      " David A. Bednar (0.0006)\n",
      "\n",
      " Quentin L. Cook (0.0003)\n",
      "\n",
      "2021\n",
      " Russell M. Nelson (0.4593)\n",
      "\n",
      " Dallin H. Oaks (0.2415)\n",
      "\n",
      " M. Russell Ballard (0.1415)\n",
      "\n",
      " Jeffrey R. Holland (0.0744)\n",
      "\n",
      " Henry B. Eyring (0.038)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0215)\n",
      "\n",
      " David A. Bednar (0.0115)\n",
      "\n",
      " Quentin L. Cook (0.0056)\n",
      "\n",
      " D. Todd Christofferson (0.0037)\n",
      "\n",
      " Neil L. Andersen (0.0017)\n",
      "\n",
      " Ronald A. Rasband (0.0008)\n",
      "\n",
      " other (0.0003)\n",
      "\n",
      " Dale G. Renlund (0.0001)\n",
      "\n",
      " Gary E. Stevenson (0.0001)\n",
      "\n",
      "2022\n",
      " Russell M. Nelson (0.2593)\n",
      "\n",
      " Dallin H. Oaks (0.1952)\n",
      "\n",
      " M. Russell Ballard (0.1424)\n",
      "\n",
      " Jeffrey R. Holland (0.1082)\n",
      "\n",
      " Henry B. Eyring (0.0755)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0584)\n",
      "\n",
      " David A. Bednar (0.0445)\n",
      "\n",
      " Quentin L. Cook (0.0298)\n",
      "\n",
      " D. Todd Christofferson (0.0228)\n",
      "\n",
      " other (0.0188)\n",
      "\n",
      " Neil L. Andersen (0.017)\n",
      "\n",
      " Ronald A. Rasband (0.013)\n",
      "\n",
      " Gary E. Stevenson (0.0082)\n",
      "\n",
      " Dale G. Renlund (0.0069)\n",
      "\n",
      "2023\n",
      " other (0.1843)\n",
      "\n",
      " Russell M. Nelson (0.1256)\n",
      "\n",
      " Dallin H. Oaks (0.1078)\n",
      "\n",
      " M. Russell Ballard (0.089)\n",
      "\n",
      " Jeffrey R. Holland (0.086)\n",
      "\n",
      " Henry B. Eyring (0.0718)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0621)\n",
      "\n",
      " David A. Bednar (0.0547)\n",
      "\n",
      " Quentin L. Cook (0.0507)\n",
      "\n",
      " D. Todd Christofferson (0.0443)\n",
      "\n",
      " Neil L. Andersen (0.0381)\n",
      "\n",
      " Ronald A. Rasband (0.0346)\n",
      "\n",
      " Gary E. Stevenson (0.0287)\n",
      "\n",
      " Dale G. Renlund (0.0223)\n",
      "\n",
      "2024\n",
      " other (0.5295)\n",
      "\n",
      " Russell M. Nelson (0.0507)\n",
      "\n",
      " Dallin H. Oaks (0.0471)\n",
      "\n",
      " M. Russell Ballard (0.0429)\n",
      "\n",
      " Jeffrey R. Holland (0.0401)\n",
      "\n",
      " Henry B. Eyring (0.0385)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0379)\n",
      "\n",
      " David A. Bednar (0.0346)\n",
      "\n",
      " Neil L. Andersen (0.0325)\n",
      "\n",
      " Ronald A. Rasband (0.0315)\n",
      "\n",
      " D. Todd Christofferson (0.0313)\n",
      "\n",
      " Quentin L. Cook (0.0308)\n",
      "\n",
      " Gary E. Stevenson (0.0266)\n",
      "\n",
      " Dale G. Renlund (0.026)\n",
      "\n",
      "2025\n",
      " other (0.8298)\n",
      "\n",
      " Russell M. Nelson (0.0165)\n",
      "\n",
      " Henry B. Eyring (0.014)\n",
      "\n",
      " Neil L. Andersen (0.0136)\n",
      "\n",
      " M. Russell Ballard (0.0135)\n",
      "\n",
      " Dallin H. Oaks (0.0134)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0133)\n",
      "\n",
      " Ronald A. Rasband (0.0129)\n",
      "\n",
      " Quentin L. Cook (0.0128)\n",
      "\n",
      " David A. Bednar (0.0125)\n",
      "\n",
      " D. Todd Christofferson (0.0124)\n",
      "\n",
      " Jeffrey R. Holland (0.012)\n",
      "\n",
      " Gary E. Stevenson (0.0117)\n",
      "\n",
      " Dale G. Renlund (0.0116)\n",
      "\n",
      "2026\n",
      " other (0.9555)\n",
      "\n",
      " David A. Bednar (0.0041)\n",
      "\n",
      " Jeffrey R. Holland (0.0036)\n",
      "\n",
      " Neil L. Andersen (0.0035)\n",
      "\n",
      " Dallin H. Oaks (0.0035)\n",
      "\n",
      " Russell M. Nelson (0.0035)\n",
      "\n",
      " Gary E. Stevenson (0.0035)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0034)\n",
      "\n",
      " Henry B. Eyring (0.0034)\n",
      "\n",
      " D. Todd Christofferson (0.0034)\n",
      "\n",
      " M. Russell Ballard (0.0033)\n",
      "\n",
      " Ronald A. Rasband (0.0032)\n",
      "\n",
      " Quentin L. Cook (0.0031)\n",
      "\n",
      " Dale G. Renlund (0.003)\n",
      "\n",
      "2027\n",
      " other (0.9926)\n",
      "\n",
      " Ronald A. Rasband (0.0011)\n",
      "\n",
      " Dale G. Renlund (0.0008)\n",
      "\n",
      " Neil L. Andersen (0.0008)\n",
      "\n",
      " Dallin H. Oaks (0.0007)\n",
      "\n",
      " Dieter F. Uchtdorf (0.0006)\n",
      "\n",
      " Russell M. Nelson (0.0006)\n",
      "\n",
      " Gary E. Stevenson (0.0006)\n",
      "\n",
      " Quentin L. Cook (0.0005)\n",
      "\n",
      " Henry B. Eyring (0.0004)\n",
      "\n",
      " David A. Bednar (0.0004)\n",
      "\n",
      " D. Todd Christofferson (0.0003)\n",
      "\n",
      " Jeffrey R. Holland (0.0003)\n",
      "\n",
      " M. Russell Ballard (0.0003)\n",
      "\n",
      "2028\n",
      " other (0.9995)\n",
      "\n",
      " David A. Bednar (0.0001)\n",
      "\n",
      " Russell M. Nelson (0.0001)\n",
      "\n",
      " M. Russell Ballard (0.0001)\n",
      "\n",
      " D. Todd Christofferson (0.0001)\n",
      "\n",
      " Neil L. Andersen (0.0001)\n",
      "\n",
      "2029\n",
      " other (0.9999)\n",
      "\n",
      " Quentin L. Cook (0.0001)\n",
      "\n",
      "2030\n",
      " other (1.0)\n",
      "\n",
      "2031\n",
      " other (1.0)\n",
      "\n",
      "2032\n",
      " other (1.0)\n",
      "\n",
      "2033\n",
      " other (1.0)\n",
      "\n",
      "2034\n",
      " other (1.0)\n",
      "\n",
      "2035\n",
      " other (1.0)\n",
      "\n",
      "2036\n",
      " other (1.0)\n",
      "\n",
      "2037\n",
      " other (1.0)\n",
      "\n",
      "2038\n",
      " other (1.0)\n",
      "\n",
      "2039\n",
      " other (1.0)\n",
      "\n",
      "2040\n",
      " other (1.0)\n",
      "\n",
      "2041\n",
      " other (1.0)\n",
      "\n",
      "2042\n",
      " other (1.0)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "run_simulation(10000,adj_apostles,life_table)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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