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  {
   "source": [
    "# Computational checking of the girl/boy probability problem"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "source": [
    "Here I replay the classical [two child problem](https://en.wikipedia.org/wiki/Boy_or_Girl_paradox) and code it up in Python.\n",
    "\n",
    "In a nutshell, the solution changes depending on if and how we differentiate between the children (for example, whether we talk about 'older' or 'younger' child or just refering to them as 'either').\n",
    "\n",
    "I also chart the solutions while I run the simulation to see how the probabilites tend to converge to their values."
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import enum, random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Kid(enum.Enum):\n",
    "    Boy = 0\n",
    "    Girl = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_kid() -> Kid:\n",
    "    return random.choice([Kid.Boy, Kid.Girl])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "random.seed(42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "both_girls = 0\n",
    "older_girl = 0\n",
    "either_girl = 0\n",
    "\n",
    "results = []\n",
    "\n",
    "for _ in range(1000):\n",
    "    younger = random_kid()\n",
    "    older = random_kid()\n",
    "\n",
    "    if older == Kid.Girl:\n",
    "        older_girl += 1\n",
    "    \n",
    "    if older == Kid.Girl and younger == Kid.Girl:\n",
    "        both_girls += 1\n",
    "    \n",
    "    if older == Kid.Girl or younger == Kid.Girl:\n",
    "        either_girl += 1\n",
    "\n",
    "    try:\n",
    "        p_both_older = both_girls / older_girl\n",
    "    except ZeroDivisionError:\n",
    "        p_both_older = 0\n",
    "    \n",
    "    try: \n",
    "        p_both_either = both_girls / either_girl\n",
    "    except ZeroDivisionError:\n",
    "        p_both_either = 0\n",
    "\n",
    "    results.append([younger.name, older.name, both_girls, older_girl, either_girl, p_both_either, p_both_older])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import altair as alt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_results = pd.DataFrame(results, columns=['younger', 'older', 'both girls', 'older girl', 'either girl', 'P(Both|Either)', 'P(Both|Older)']).reset_index()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "     index younger older  both girls  older girl  either girl  P(Both|Either)  \\\n0        0     Boy   Boy           0           0            0        0.000000   \n1        1    Girl   Boy           0           0            1        0.000000   \n2        2     Boy   Boy           0           0            1        0.000000   \n3        3     Boy   Boy           0           0            1        0.000000   \n4        4    Girl   Boy           0           0            2        0.000000   \n..     ...     ...   ...         ...         ...          ...             ...   \n995    995    Girl   Boy         263         513          763        0.344692   \n996    996    Girl  Girl         264         514          764        0.345550   \n997    997    Girl  Girl         265         515          765        0.346405   \n998    998    Girl   Boy         265         515          766        0.345953   \n999    999    Girl  Girl         266         516          767        0.346806   \n\n     P(Both|Older)  \n0         0.000000  \n1         0.000000  \n2         0.000000  \n3         0.000000  \n4         0.000000  \n..             ...  \n995       0.512671  \n996       0.513619  \n997       0.514563  \n998       0.514563  \n999       0.515504  \n\n[1000 rows x 8 columns]",
      "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>index</th>\n      <th>younger</th>\n      <th>older</th>\n      <th>both girls</th>\n      <th>older girl</th>\n      <th>either girl</th>\n      <th>P(Both|Either)</th>\n      <th>P(Both|Older)</th>\n    </tr>\n  </thead>\n  <tbody>\n    <tr>\n      <th>0</th>\n      <td>0</td>\n      <td>Boy</td>\n      <td>Boy</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>1</th>\n      <td>1</td>\n      <td>Girl</td>\n      <td>Boy</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>2</th>\n      <td>2</td>\n      <td>Boy</td>\n      <td>Boy</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>3</th>\n      <td>3</td>\n      <td>Boy</td>\n      <td>Boy</td>\n      <td>0</td>\n      <td>0</td>\n      <td>1</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>4</th>\n      <td>4</td>\n      <td>Girl</td>\n      <td>Boy</td>\n      <td>0</td>\n      <td>0</td>\n      <td>2</td>\n      <td>0.000000</td>\n      <td>0.000000</td>\n    </tr>\n    <tr>\n      <th>...</th>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n      <td>...</td>\n    </tr>\n    <tr>\n      <th>995</th>\n      <td>995</td>\n      <td>Girl</td>\n      <td>Boy</td>\n      <td>263</td>\n      <td>513</td>\n      <td>763</td>\n      <td>0.344692</td>\n      <td>0.512671</td>\n    </tr>\n    <tr>\n      <th>996</th>\n      <td>996</td>\n      <td>Girl</td>\n      <td>Girl</td>\n      <td>264</td>\n      <td>514</td>\n      <td>764</td>\n      <td>0.345550</td>\n      <td>0.513619</td>\n    </tr>\n    <tr>\n      <th>997</th>\n      <td>997</td>\n      <td>Girl</td>\n      <td>Girl</td>\n      <td>265</td>\n      <td>515</td>\n      <td>765</td>\n      <td>0.346405</td>\n      <td>0.514563</td>\n    </tr>\n    <tr>\n      <th>998</th>\n      <td>998</td>\n      <td>Girl</td>\n      <td>Boy</td>\n      <td>265</td>\n      <td>515</td>\n      <td>766</td>\n      <td>0.345953</td>\n      <td>0.514563</td>\n    </tr>\n    <tr>\n      <th>999</th>\n      <td>999</td>\n      <td>Girl</td>\n      <td>Girl</td>\n      <td>266</td>\n      <td>516</td>\n      <td>767</td>\n      <td>0.346806</td>\n      <td>0.515504</td>\n    </tr>\n  </tbody>\n</table>\n<p>1000 rows × 8 columns</p>\n</div>"
     },
     "metadata": {},
     "execution_count": 8
    }
   ],
   "source": [
    "df_results"
   ]
  },
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   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "      index       variable     value         type\n0         0        younger       Boy          NaN\n1         1        younger      Girl          NaN\n2         2        younger       Boy          NaN\n3         3        younger       Boy          NaN\n4         4        younger      Girl          NaN\n...     ...            ...       ...          ...\n6995    995  P(Both|Older)  0.512671  probability\n6996    996  P(Both|Older)  0.513619  probability\n6997    997  P(Both|Older)  0.514563  probability\n6998    998  P(Both|Older)  0.514563  probability\n6999    999  P(Both|Older)  0.515504  probability\n\n[7000 rows x 4 columns]",
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     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "to_plot = df_results.melt(id_vars='index')\n",
    "to_plot.loc[to_plot['variable'].isin(['both girls', 'older girl', 'either girl']), 'type']  = 'count'\n",
    "to_plot.loc[to_plot['variable'].isin(['P(Both|Either)', 'P(Both|Older)']), 'type']  = 'probability'\n",
    "to_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
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{\"index\": 995, \"variable\": \"either girl\", \"value\": 763, \"type\": \"count\"}, {\"index\": 996, \"variable\": \"either girl\", \"value\": 764, \"type\": \"count\"}, {\"index\": 997, \"variable\": \"either girl\", \"value\": 765, \"type\": \"count\"}, {\"index\": 998, \"variable\": \"either girl\", \"value\": 766, \"type\": \"count\"}, {\"index\": 999, \"variable\": \"either girl\", \"value\": 767, \"type\": \"count\"}]}}, {\"mode\": \"vega-lite\"});\n</script>",
      "text/plain": "alt.LayerChart(...)"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "chart = alt.Chart(to_plot).encode(alt.X('index:Q'))\n",
    "\n",
    "label = alt.selection_single(encodings=['x'], on='mouseover', nearest=True, empty='none')\n",
    "\n",
    "count_chart = alt.Chart(data=to_plot[to_plot['type'] == 'count']).mark_line().encode(\n",
    "    alt.X('index:Q'), alt.Y('value:Q'), color=alt.Color('variable:N'), \n",
    ")\n",
    "\n",
    "probablity_chart = alt.Chart(to_plot[to_plot['type'] == 'probability']).mark_line().encode(\n",
    "    alt.X('index:Q'), alt.Y('value:Q'), color=alt.Color('variable:N')\n",
    ")\n",
    "\n",
    "values_chart = alt.layer(\n",
    "    probablity_chart.add_selection(label),\n",
    "    probablity_chart.mark_rule(color='gray').encode(alt.X('index:Q')).transform_filter(label),\n",
    "    count_chart,\n",
    ").resolve_scale(y='independent').properties(width=600)\n",
    "\n",
    "values_chart"
   ]
  }
 ]
}