Birthday problem.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "68578bc0",
   "metadata": {},
   "source": [
    "# Birthday problem"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e8229204",
   "metadata": {},
   "source": [
    "How many people in a room so that at least two of them share the same birthday?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "85a0aa5d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set_style('whitegrid')\n",
    "sns.set_context('poster')\n",
    "\n",
    "from matplotlib import pyplot as plt\n",
    "from joblib import Parallel, delayed\n",
    "from tqdm import tqdm\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1af7387",
   "metadata": {},
   "source": [
    "# one time simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "939ae785",
   "metadata": {},
   "outputs": [],
   "source": [
    "N = 20\n",
    "simulations = np.random.randint(low = 1, high = 356, size = (int(1e4),20),)\n",
    "counter = [len(set(item)) != len(item) for item in simulations]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e72dbb9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4173"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(counter)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "be7d746f",
   "metadata": {},
   "source": [
    "# make it a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1141f053",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulation(n_people:int,n_sim:int) -> float:\n",
    "    simulations = np.random.randint(low = 1, high = 356, size = (int(n_sim),n_people),)\n",
    "    counter = [len(set(item)) != len(item) for item in simulations]\n",
    "    return np.mean(counter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "93e73989",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████| 99/99 [02:59<00:00,  1.81s/it]\n"
     ]
    }
   ],
   "source": [
    "n_simulations = int(1e2)\n",
    "n_people = np.arange(2,100 + 1,)\n",
    "df = []\n",
    "for n_p in tqdm(n_people):\n",
    "    res = Parallel(n_jobs = -1,verbose = 0)(delayed(simulation)(**{'n_people':n_p,'n_sim':int(1e4)}) for _ in range(n_simulations))\n",
    "    df_temp = pd.DataFrame(np.array(res).reshape(-1,1),columns = ['proportion'])\n",
    "    df_temp['people'] = n_p\n",
    "    df.append(df_temp)\n",
    "df = pd.concat(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "db5916b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f2cc352f7f0>"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig,ax = plt.subplots(figsize = (20,8))\n",
    "ax = sns.pointplot(x = 'people',y = 'proportion',data = df,\n",
    "                   capsize = .1,seed = 12345,\n",
    "                   markers = '.',\n",
    "                   ax = ax)\n",
    "_ = ax.set(xlabel = 'number of people', ylabel = 'Proportion of a pair',\n",
    "           xticks = np.arange(100 + 1,step = 10),\n",
    "           xticklabels = np.arange(100 + 1,step = 10),)\n",
    "ax.axhline(0.5,linestyle = '--',color = 'black',label = 'p = 0.5')\n",
    "for k in [20,21,22,23]:\n",
    "    ax.axvline(k,linestyle = '--',color = 'red',label = f'{k} people in the room')\n",
    "ax.legend(loc = 'best')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "9d01efbc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<img src=\"https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2020/04/GraphBirthdayProbabilities2.png?w=568&ssl=1\"/>"
      ],
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import Image\n",
    "from IPython.core.display import HTML \n",
    "Image(url= \"https://i0.wp.com/statisticsbyjim.com/wp-content/uploads/2020/04/GraphBirthdayProbabilities2.png?w=568&ssl=1\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "dfba4c1a",
   "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 tr th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe thead tr:last-of-type th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th colspan=\"8\" halign=\"left\">proportion</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>people</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.002842</td>\n",
       "      <td>0.000506</td>\n",
       "      <td>0.0014</td>\n",
       "      <td>0.002500</td>\n",
       "      <td>0.00280</td>\n",
       "      <td>0.0032</td>\n",
       "      <td>0.0045</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.008381</td>\n",
       "      <td>0.000822</td>\n",
       "      <td>0.0064</td>\n",
       "      <td>0.007775</td>\n",
       "      <td>0.00845</td>\n",
       "      <td>0.0090</td>\n",
       "      <td>0.0102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.016966</td>\n",
       "      <td>0.001367</td>\n",
       "      <td>0.0133</td>\n",
       "      <td>0.016075</td>\n",
       "      <td>0.01680</td>\n",
       "      <td>0.0180</td>\n",
       "      <td>0.0204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.028131</td>\n",
       "      <td>0.001706</td>\n",
       "      <td>0.0240</td>\n",
       "      <td>0.027000</td>\n",
       "      <td>0.02820</td>\n",
       "      <td>0.0293</td>\n",
       "      <td>0.0332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.041542</td>\n",
       "      <td>0.002058</td>\n",
       "      <td>0.0357</td>\n",
       "      <td>0.040000</td>\n",
       "      <td>0.04155</td>\n",
       "      <td>0.0430</td>\n",
       "      <td>0.0485</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>96</th>\n",
       "      <td>100.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>97</th>\n",
       "      <td>100.0</td>\n",
       "      <td>0.999999</td>\n",
       "      <td>0.000010</td>\n",
       "      <td>0.9999</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>100.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99</th>\n",
       "      <td>100.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>100</th>\n",
       "      <td>100.0</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.00000</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.0000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>99 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       proportion                                                         \\\n",
       "            count      mean       std     min       25%      50%     75%   \n",
       "people                                                                     \n",
       "2           100.0  0.002842  0.000506  0.0014  0.002500  0.00280  0.0032   \n",
       "3           100.0  0.008381  0.000822  0.0064  0.007775  0.00845  0.0090   \n",
       "4           100.0  0.016966  0.001367  0.0133  0.016075  0.01680  0.0180   \n",
       "5           100.0  0.028131  0.001706  0.0240  0.027000  0.02820  0.0293   \n",
       "6           100.0  0.041542  0.002058  0.0357  0.040000  0.04155  0.0430   \n",
       "...           ...       ...       ...     ...       ...      ...     ...   \n",
       "96          100.0  1.000000  0.000000  1.0000  1.000000  1.00000  1.0000   \n",
       "97          100.0  0.999999  0.000010  0.9999  1.000000  1.00000  1.0000   \n",
       "98          100.0  1.000000  0.000000  1.0000  1.000000  1.00000  1.0000   \n",
       "99          100.0  1.000000  0.000000  1.0000  1.000000  1.00000  1.0000   \n",
       "100         100.0  1.000000  0.000000  1.0000  1.000000  1.00000  1.0000   \n",
       "\n",
       "                \n",
       "           max  \n",
       "people          \n",
       "2       0.0045  \n",
       "3       0.0102  \n",
       "4       0.0204  \n",
       "5       0.0332  \n",
       "6       0.0485  \n",
       "...        ...  \n",
       "96      1.0000  \n",
       "97      1.0000  \n",
       "98      1.0000  \n",
       "99      1.0000  \n",
       "100     1.0000  \n",
       "\n",
       "[99 rows x 8 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.groupby(['people']).describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8b8403b1",
   "metadata": {},
   "source": [
    "This simulation overcalculate the proportions, and I don't know why. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b03295c4",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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