9 red 1 white.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import random\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "sns.set_style('white')\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given you have 9 reds and 1 white marbles in a bag, you and your 9 friends take out 1 marble out of the bag. Whoever has got the white one wins. Which position has the highest chance to win?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0,0.5,'Counts'),\n",
       " Text(0.5,0,'Position wins'),\n",
       " Text(0.5,1,'time of wins if on different position')]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2be34e8c208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bag = np.concatenate([['red']*29,['white']*1])\n",
    "bag\n",
    "\n",
    "results = np.array([np.random.choice(bag,size=bag.shape[0],replace=False) for ii in range(int(1e5))])\n",
    "\n",
    "fig,ax = plt.subplots(figsize=(8,5))\n",
    "ax.hist(np.where(results == 'white')[1],bins=range(len(bag)+1),rwidth=.5,normed=True)\n",
    "#sns.kdeplot(np.where(results == 'white')[1],shade=True,ax=ax,kernel='gau',bw=0.1,cut=0,)\n",
    "ax.set(xlabel='Position wins',ylabel='Counts',title='time of wins if on different position')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What if there are 8 reds and 2 whites?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0,0.5,'Counts'),\n",
       " Text(0.5,0,'Position wins'),\n",
       " Text(0.5,1,'time of wins if on different position')]"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2be33c60240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bag = np.concatenate([['red']*28,['white']*2])\n",
    "bag\n",
    "\n",
    "results = np.array([np.random.choice(bag,size=bag.shape[0],replace=False) for ii in range(int(1e5))])\n",
    "positions = [next((ii for ii,x in enumerate(row) if (x == 'white')), None) for row in results]\n",
    "fig,ax = plt.subplots(figsize=(8,5))\n",
    "ax.hist(positions,bins=range(len(bag)+1),rwidth=.5,normed=True)\n",
    "#sns.kdeplot(positions,shade=True,ax=ax,bw=1,cut=0)\n",
    "ax.set(xlabel='Position wins',ylabel='Counts',title='time of wins if on different position')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How about 7 reds and 3 whites?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0,0.5,'Counts'),\n",
       " Text(0.5,0,'Position wins'),\n",
       " Text(0.5,1,'time of wins if on different position')]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2be34e845c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bag = np.concatenate([['red']*27,['white']*3])\n",
    "results = np.array([np.random.choice(bag,size=bag.shape[0],replace=False) for ii in range(int(1e5))])\n",
    "positions = [next((ii for ii,x in enumerate(row) if (x == 'white')), None) for row in results]\n",
    "fig,ax = plt.subplots(figsize=(8,5))\n",
    "ax.hist(positions,bins=range(len(bag)+1),rwidth=.5,normed=True)\n",
    "#sns.kdeplot(positions,shade=True,ax=ax,bw=1,cut=0)\n",
    "ax.set(xlabel='Position wins',ylabel='Counts',title='time of wins if on different position')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bags(reds = 10,whites = 10, sim_time = int(1e5)):\n",
    "    bag = np.concatenate([['red']*reds,['white']*whites])\n",
    "    results = np.array([np.random.choice(bag,size=bag.shape[0],replace=False) for ii in range(sim_time)])\n",
    "    positions = [next((ii for ii,x in enumerate(row) if (x == 'white')), None) for row in results]\n",
    "    fig,ax = plt.subplots(figsize=(8,5))\n",
    "    ax.hist(positions,bins=range(len(bag)+1),rwidth=.5,normed=True)\n",
    "    #sns.kdeplot(positions,shade=True,ax=ax,bw=1,cut=0)\n",
    "    ax.set(xlabel='Position wins',ylabel='Probability to win',title='{} whites and {} reds'.format(whites,reds))\n",
    "    return results,positions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2be393cadd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "results,positions = bags(25,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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