Jessime/Airplane_Seat.ipynb

## Airplane_Seat.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Will Someone Be Sitting In Your Seat On The Plane?\n",
    "\n",
    "This riddle was originally posted at:\n",
    "\n",
    "http://fivethirtyeight.com/features/will-someone-be-sitting-in-your-seat-on-the-plane/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prompt\n",
    "\n",
    "There’s an airplane with 100 seats, and there are 100 ticketed passengers each with an assigned seat. They line up to board in some random order. However, the first person to board is the worst person alive, and just sits in a random seat, without even looking at his boarding pass. Each subsequent passenger sits in his or her own assigned seat if it’s empty, but sits in a random open seat if the assigned seat is occupied. What is the probability that you, the hundredth passenger to board, finds your seat unoccupied?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Creating a simulation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class Simulation(object):\n",
    "    \n",
    "    def __init__(self):\n",
    "        self.open_seats = set(range(100))\n",
    "        self.occupied_seats = set()\n",
    "        self.your_seat_number = random.choice(list(self.open_seats))\n",
    "        self.your_seat_free = True\n",
    "        self.other_people = set(range(100))\n",
    "        self.other_people.remove(self.your_seat_number)\n",
    "\n",
    "    def sit_in_seat(self, seat_number):\n",
    "        \"\"\"When a seat is sat it, it moves from open to occupied.\"\"\"\n",
    "        self.open_seats.remove(seat_number)\n",
    "        self.occupied_seats.add(seat_number)\n",
    "        \n",
    "    def pick_random_seat(self):\n",
    "        \"\"\"The first person, and all other people with occupied seats, sit is a random seat.\"\"\"\n",
    "        chosen_seat = random.choice(list(self.open_seats))\n",
    "        self.sit_in_seat(chosen_seat)\n",
    "        \n",
    "    def pick_first_seat(self):\n",
    "        \"\"\"The first person has different rules than everyone else.\n",
    "        He automatically picks his seat at random.\"\"\"\n",
    "        self.pick_random_seat()\n",
    "        first_person_number = random.choice(list(self.other_people))\n",
    "        self.other_people.remove(first_person_number)\n",
    "        \n",
    "    def pick_other_seats(self, person):\n",
    "        \"\"\"The 98 people in the middle all follow the same rule.\n",
    "        If their seat is open, they will sit in that seat.\n",
    "        Otherwise, they'll pick a random seat to sit in.\"\"\"\n",
    "        if person in self.open_seats:\n",
    "            self.sit_in_seat(person)\n",
    "        else:\n",
    "            self.pick_random_seat()\n",
    "        \n",
    "    def simulate(self):\n",
    "        \"\"\"A single simulation consists of three steps.\n",
    "        1. Pick the first seat at random.\n",
    "        2. Seat all the other people according to rules.\n",
    "        3. Check if your seat is open.\"\"\"\n",
    "        self.pick_first_seat()\n",
    "        \n",
    "        for person in self.other_people:\n",
    "            self.pick_other_seats(person)\n",
    "            \n",
    "        if self.your_seat_number not in self.open_seats:\n",
    "            self.your_seat_free = False\n",
    "        return self.your_seat_free"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Running a bunch of simulations\n",
    "\n",
    "To get the probability of your seat being free, we need to run the simulation a large number of times. The fraction of the time that your seat is free over the course of all the trials is equivalent to the probability that it'll be free for any given run."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from tqdm import trange"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def run_bunch():\n",
    "    number_of_simulations = 10000\n",
    "    sucesses = 0\n",
    "    for i in xrange(number_of_simulations):\n",
    "        if Simulation().simulate() == True:\n",
    "            sucesses += 1\n",
    "    return sucesses/float(number_of_simulations)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49789"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "run_bunch()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Runing a bunch of bunches\n",
    "\n",
    "Instead of running 10,000,000 times, it might be more informative (or at least visually nicer) to get a distribution of probabilities which can then be plotted. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "plt.style.use(\"ggplot\")\n",
    "plt.rcParams['figure.figsize'] = [9.0, 6.0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "results = [run_bunch() for i in trange(10000)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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FF14gMzOTxx9/nISEBAYNGkS7du28GUVEREQqCa8WM61bt6Z58+YAVK9enZyc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\ndzhaLpsQLUTd+iv05kz0xxnoAcPkKj7hFaSZEeI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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8ca52dc390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(results, bins=30)\n",
    "plt.title('Distributions of Probabilities You\\'ll Get Your Seat', fontsize=16)\n",
    "plt.xlabel('Probability', fontsize=14)\n",
    "plt.ylabel('Density', fontsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "More trials would smooth out the graph a bit more, but it's pretty obvious that the simulation is saying that your seat will be free 50% of the time."
   ]
  }
 ],
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