Stat_exercise.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Задача\n",
    "\n",
    "Среди 25 Экзаменационных билетов 5 \"хороших\". Два студента по очереди берут по одному билету. Первый берет с равной вероятностью из 25 билетов, второй из оставшихся.\n",
    "Найти вероятность того, что второй студент взял хороший билет."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline\n",
    "import numpy as np\n",
    "from tqdm import tqdm\n",
    "\n",
    "def run_simulation(n_simulations:int):\n",
    "    results = []\n",
    "    for i in range(n_simulations):\n",
    "        np.random.seed(i)\n",
    "        # create array of tickets\n",
    "        tickets = np.concatenate([np.zeros(20), np.ones(5)])\n",
    "        # shuffle it\n",
    "        np.random.shuffle(tickets)\n",
    "\n",
    "        # first person choice - index in the array\n",
    "        first_choice = np.random.choice(range(len(tickets)), 1)[0]\n",
    "        # remove that ticket by it's index from the remain tickets\n",
    "        tickets = np.delete(tickets, first_choice)\n",
    "        # second choice\n",
    "        second_choice = np.random.choice(tickets, 1)[0]\n",
    "        results.append(second_choice)\n",
    "    return np.sum(results)/len(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Running simulations: 100%|██████████| 499/499 [22:27<00:00,  5.20s/it]\n"
     ]
    }
   ],
   "source": [
    "results = []\n",
    "steps = np.arange(100, 50000, 100)\n",
    "\n",
    "for n in tqdm(steps, desc='Running simulations'):\n",
    "    results.append(run_simulation(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Simulation results')"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pylab.figure(figsize=(16,8))\n",
    "pylab.scatter(steps, results)\n",
    "pylab.plot(steps, results)\n",
    "pylab.axhline(0.20, color='r', linestyle='--')\n",
    "pylab.xlabel('Number of simulations', size=16)\n",
    "pylab.ylabel('Second person win ratio', size=16)\n",
    "pylab.title('Simulation results', size=18)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}