abhinavtripathi95/coin_sim.ipynb

## coin_sim.ipynb
{
  "cells": [
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "# Problem: \nYou have 9 fair coins and 1 baised coin. The chances of getting heads for the biased coin is 90%. Given that after 10 tosses we get 9 heads, what are the chances that the chosen coin is biased?"
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "Let's do a million trails of choosing 1 coin and tossing it 10 times. Then we find out how many times we get 9 heads in case of fair coin, and how many times we get 9 heads in case of biased coin."
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "import numpy as np\nimport matplotlib.pyplot as plt",
      "execution_count": 1,
      "outputs": []
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Choose one of the 10 coins at random"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# let's do a million trials\ncoin_choice = np.random.randint(10, size = int(1e6))\ncoin_choice",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 2,
          "data": {
            "text/plain": "array([5, 7, 0, ..., 5, 9, 9])"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "plt.hist(coin_choice, bins= np.arange(0,11))\nplt.title(\"Frequency of Coin Chosen\")\nplt.show()",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "## Flip the coin 10 times"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "# 0 = biased coin\n# 1-9 = fair coin\nbiased_heads = []\nfair_heads = []\n\n# for every coin choice get 10 trials\nfor coin in coin_choice:\n    if coin == 0:\n        biased_heads.append((np.random.randint(10, size=10)>0).astype(int).sum())\n    else:\n        fair_heads.append(np.random.randint(2, size=10).sum())",
      "execution_count": 4,
      "outputs": []
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "n1, bin1, patch1 = plt.hist(biased_heads, bins = np.arange(0,12))\nplt.title(\"Number of Heads for Biased Coin\")\nplt.show()",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAEICAYAAAC9E5gJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAdN0lEQVR4nO3df7TVdZ3v8edLEH+hgnJ0FFBIGROt0E7KZDPX1Iuo3YFZSyecUjKKcnCyGacRW63w54x2pzTXMouSAFORa3YlwyGuPypvqRzUVCSHM0hyhOQoP8S8atj7/vF9n/x62OecfX5wNpzzeqy11/7u9/fz+e7Pdx/Yr/39sb9bEYGZmfVvu9V6AGZmVnsOAzMzcxiYmZnDwMzMcBiYmRkOAzMzw2FgXSRprqSra/TckvR9SZskPVaLMbQaz8mSmrrQby9JP5a0RdL/2hFjq/Ccr0l6T288Vz7fKEkhaeAOWPZfSnqup5fbXzkM+ghJayS9JGmfUu0zkh6q4bB2lI8A/x0YEREntJ4p6VOSHq5QXyPptN4YYJXOBg4GDoyIc7q7sAylP+Yb/muSXpR0RblNRAyOiNXdfa6eJOnvJDXkmNdLuk/SRzrqFxG/iIijemOM/YHDoG8ZCFxc60F0lqQBnexyOLAmIn6/I8bTiw4H/jMitnW2YzuftNflG/5gitCcJmlydwa5I0n6J+AG4F8pgvEw4FvApFqOqz9yGPQt/xP4Z0lDWs+otLku6SFJn8npT0n6v5Kul7RZ0mpJH876WkkbJE1ttdhhkpZK2irpZ5IOLy37vTlvo6TnJP1tad5cSTdLWizp98BHK4z3UEmLsn+jpM9mfRrwPeAv8pPkFa37VkvSpyWtzN1NS1qN/5u53q9KWi7pL0vz9sp12CTpWeBDrZZ7aX4q35rrfmqF574C+Crw8VyPaZJ2k/QVSb/N13u+pP2zfcvfb5qkF4AHOlq/iHge+CUwtvS8IenInD5L0hO5jmslXV5qt6ekH0h6Jf89LJN0cM7bX9It+Sn+RUlXtwS6pAGS/l3Sy5JWA2e18/rvD1wJzIiIuyPi9xHxh4j4cUR8KdvsIekGSevydoOkPXLeu3bP5ZbfP0t6SsWutzsl7dnR62QpInzrAzdgDXAacDdwddY+AzyU06OAAAaW+jwEfCanPwVsAy4ABgBXAy8ANwF7ABOArcDgbD83H/9Vzv8m8HDO2wdYm8saCBwPvAwcU+q7BTiJ4gPJnhXW52cUnxD3BMYBzcCppbE+3M5rUXF+y2uU05OBRuDoHONXgF+W2n4SODDnXQL8rmWcwLXAL4ADgJHAM0BTzjsq1/3Q0ut+RBvjvBz4Qenxp3NM7wEG59/y1lZ/v/n5+u5VYXknt4wjH48BXgROKdUCOLLU/n35N3g/8BIwOed9DvgxsHf+e/ggsF/O+9/Ad3IcBwGPAZ/LeZ8HfpOvywHAg7T6d1cay0SKf3PbzSu1uRJ4JJ+njiLcrmpjfdfkWA7N514JfL7W/zd3lVvNB+BbD/0h3wmDYyneaOvofBisKs17X7Y/uFR7BRiX03OBBaV5g4G3803g48AvWo3vO8CsUt/57azLyFzWvqXavwFzS2PtKAy2AZtb3f7IO2FwHzCt1Gc34HXg8DaWuQn4QE6vBiaW5k3nnTA4EtiQf4vdO/ibXc67w+B+4O9Lj48C/kARSC1/v/e0s7yTcx03A69m+7uBQaU2fwqDCv1vAK7P6U9TvPG+v1Wbg4E3KYURcC7wYE4/QOkNmOJDRFth8Angdx28Rv8FnFl6fDrFLsKW9W0dBp8sPf4a8O1a/9/cVW7eTdTHRMQzwL3AzC50f6k0/f9yea1rg0uP15ae9zVgI8WnssOBE3P3wmZJmyn+4/9Zpb4VHApsjIitpdpvgeGdWJdHImJI+UaxpdPicOCbpfFtBNTyHJIuyV1IW3L+/sCw0vjK4/9ty0RENAJfpHij3yBpgaRDqxzzoeVl5fRAijfgFu29blAcMxgSEfsBQyj+ZvMqNZR0oqQHJTVL2kLxqb5lHW8FlgALcvfM1yTtTvG67Q6sL71236H45N6yDhVfmwpeodjV2N6ZRpVek/Zez9+Vpl/n3f9erR0Og75pFvBZ3v3m2XKwde9Srfzm3BUjWyYkDabYNF9H8Wbws1ZvxoMj4sJS3/Yul7sOOEDSvqXaYRS7PHrKWopdG+Ux7hURv8zjA5cCfwsMzSDZQhEWAOsprXuO7U8i4vaI+AjFG2cA11U5pnXZp7zcbbw7pKu+zHBEbAFuB/5HG01uBxYBIyNif+Db5DpGse/+iogYC3wY+BhwPsXr9iYwrPS67RcRx+Qy231tWvkV8AbFLru2VHpN1rXT3rrIYdAH5afTO4EvlGrNFG+mn8yDfJ8GjujmU50p6SOSBgFXAY9GxFqKLZM/l3SepN3z9iFJR1c5/rUUuyj+LQ9kvh+YBtzWzfGWfRu4TNIx8KeDoi2nd+5L8SbcDAyU9FVgv1Lfhdl3qKQRwD+0zJB0lKRT8iDnGxSfzN+uckx3AP8oaXSG678Cd0YXzjbKsQwGpgAr2miyL8UW2BuSTgD+rtT3o5LelweGX6XYXfV2RKwHfgp8XdJ+edD7CEn/LbsuBL4gaYSkobSzhZph9VXgJkmTJe2d/1bOkPS10mvyFUl1koZl+x905fWw9jkM+q4rKQ7wlX0W+BLF5vkxFG+43XE7xVbIRooDjJ8AyN07EyjeiNZRbLpfR3GguVrnUuwnXwf8iOJ4w9JujvdPIuJHOaYFkl6lOAh8Rs5eQnFM4T8pdku8wbt3fVyR9ecp3hhvLc3bg+IA88sU630Q8OUqhzUnl/XzXPYblIKmSofm2Umv5RgPIP8uFfw9cKWkrRRvsgtL8/4MuIsiCFZSHNBveRM+HxgEPEtxLOUu4JCc912K1+/XwOMUxyzaFBHfAP6J4gB+M8XrfBHFQWooTmRoAJ4Cns5l1uTLjn2d8kCLmZn1Y94yMDMzh4GZmTkMzMwMh4GZmVF8oaUqeYpZA/BiRHxM0mhgAcXZCo8D50XEW3lK3XyKs0teAT4eEWtyGZdRnCL4NvCFiFiS9YkUlzMYAHwvIq7taDzDhg2LUaNGVTt8MzMDli9f/nJE1LWud+Ya4xdTnGLWcr71dRRfXV8g6dsUb/I35/2miDhS0pRs93FJYylONTyG4huE/0fSn+eybqK4JHETsEzSooh4tr3BjBo1ioaGhk4M38zMJFX8VnhVu4nyizVnUVwtEkkCTqE4vxiKr7u3fItwEu98/f0u4NRsP4niWjZvRnE1xUbghLw1RsTqiHiLYmvDl681M+tF1R4zuAH4F4qLYEFxNcfNpW9GNvHOpQ+Gk1/Qyflbsv2f6q36tFXfjqTpKn4Eo6G5ubnKoZuZWUc6DANJHwM2RMTycrlC0+hgXmfr2xcjZkdEfUTU19Vtt8vLzMy6qJpjBicBfy3pTIpry+9HsaUwRNLA/PQ/gncuHtVEcaGqprwa4f4Ulytoqbco92mrbmZmvaDDLYOIuCwiRkTEKIoDwA9ExCcofrTi7Gw2FbgnpxflY3L+A1Fc82IRMCV/uWg0xQ9vPAYsA8bkxbkG5XMs6pG1MzOzqnTmbKLWLqW4yNfVwBPALVm/BbhVUiPFFsEUgIhYIWkhxcWttlH81N3bAJIuori41QBgTkS0dZVFMzPbAXbZC9XV19eHTy01M+scScsjor513d9ANjMzh4GZmXXvmIGZ2U5p1Myf9Orzrbn2rF59vh3BWwZmZuYwMDMzh4GZmeEwMDMzHAZmZobDwMzMcBiYmRkOAzMzw2FgZmY4DMzMDIeBmZnhMDAzMxwGZmaGw8DMzHAYmJkZVYSBpD0lPSbp15JWSLoi63MlPS/pybyNy7ok3SipUdJTko4vLWuqpFV5m1qqf1DS09nnRknaEStrZmaVVfPjNm8Cp0TEa5J2Bx6WdF/O+1JE3NWq/RnAmLydCNwMnCjpAGAWUA8EsFzSoojYlG2mA48Ai4GJwH2YmVmv6HDLIAqv5cPd8xbtdJkEzM9+jwBDJB0CnA4sjYiNGQBLgYk5b7+I+FVEBDAfmNyNdTIzs06q6mcvJQ0AlgNHAjdFxKOSLgSukfRV4H5gZkS8CQwH1pa6N2WtvXpThXqlcUyn2ILgsMMOq2boZmY7XG/+zOaO+onNqg4gR8TbETEOGAGcIOlY4DLgvcCHgAOAS7N5pf390YV6pXHMjoj6iKivq6urZuhmZlaFTp1NFBGbgYeAiRGxPncFvQl8HzghmzUBI0vdRgDrOqiPqFA3M7NeUs3ZRHWShuT0XsBpwG9yXz955s9k4Jnssgg4P88qGg9siYj1wBJggqShkoYCE4AlOW+rpPG5rPOBe3p2Nc3MrD3VHDM4BJiXxw12AxZGxL2SHpBUR7Gb50ng89l+MXAm0Ai8DlwAEBEbJV0FLMt2V0bExpy+EJgL7EVxFpHPJDIz60UdhkFEPAUcV6F+ShvtA5jRxrw5wJwK9Qbg2I7GYmZmO4a/gWxmZg4DMzNzGJiZGQ4DMzPDYWBmZjgMzMwMh4GZmeEwMDMzHAZmZobDwMzMcBiYmRkOAzMzw2FgZmY4DMzMDIeBmZnhMDAzMxwGZmaGw8DMzKgiDCTtKekxSb+WtELSFVkfLelRSask3SlpUNb3yMeNOX9UaVmXZf05SaeX6hOz1ihpZs+vppmZtaeaLYM3gVMi4gPAOGCipPHAdcD1ETEG2ARMy/bTgE0RcSRwfbZD0lhgCnAMMBH4lqQBkgYANwFnAGOBc7OtmZn1kg7DIAqv5cPd8xbAKcBdWZ8HTM7pSfmYnH+qJGV9QUS8GRHPA43ACXlrjIjVEfEWsCDbmplZL6nqmEF+gn8S2AAsBf4L2BwR27JJEzA8p4cDawFy/hbgwHK9VZ+26pXGMV1Sg6SG5ubmaoZuZmZVqCoMIuLtiBgHjKD4JH90pWZ5rzbmdbZeaRyzI6I+Iurr6uo6HriZmVWlU2cTRcRm4CFgPDBE0sCcNQJYl9NNwEiAnL8/sLFcb9WnrbqZmfWSas4mqpM0JKf3Ak4DVgIPAmdns6nAPTm9KB+T8x+IiMj6lDzbaDQwBngMWAaMybOTBlEcZF7UEytnZmbVGdhxEw4B5uVZP7sBCyPiXknPAgskXQ08AdyS7W8BbpXUSLFFMAUgIlZIWgg8C2wDZkTE2wCSLgKWAAOAORGxosfW0MzMOtRhGETEU8BxFeqrKY4ftK6/AZzTxrKuAa6pUF8MLK5ivGZmtgP4G8hmZuYwMDMzh4GZmeEwMDMzHAZmZobDwMzMcBiYmRkOAzMzw2FgZmY4DMzMDIeBmZnhMDAzMxwGZmaGw8DMzHAYmJkZDgMzM8NhYGZmOAzMzIwqwkDSSEkPSlopaYWki7N+uaQXJT2ZtzNLfS6T1CjpOUmnl+oTs9YoaWapPlrSo5JWSbpT0qCeXlEzM2tbNVsG24BLIuJoYDwwQ9LYnHd9RIzL22KAnDcFOAaYCHxL0gBJA4CbgDOAscC5peVcl8saA2wCpvXQ+pmZWRU6DIOIWB8Rj+f0VmAlMLydLpOABRHxZkQ8DzQCJ+StMSJWR8RbwAJgkiQBpwB3Zf95wOSurpCZmXVep44ZSBoFHAc8mqWLJD0laY6koVkbDqwtdWvKWlv1A4HNEbGtVb3S80+X1CCpobm5uTNDNzOzdlQdBpIGAz8EvhgRrwI3A0cA44D1wNdbmlboHl2ob1+MmB0R9RFRX1dXV+3QzcysAwOraSRpd4oguC0i7gaIiJdK878L3JsPm4CRpe4jgHU5Xan+MjBE0sDcOii3NzOzXlDN2UQCbgFWRsQ3SvVDSs3+BngmpxcBUyTtIWk0MAZ4DFgGjMkzhwZRHGReFBEBPAicnf2nAvd0b7XMzKwzqtkyOAk4D3ha0pNZ+zLF2UDjKHbprAE+BxARKyQtBJ6lOBNpRkS8DSDpImAJMACYExErcnmXAgskXQ08QRE+ZmbWSzoMg4h4mMr79Re30+ca4JoK9cWV+kXEaoqzjczMrAb8DWQzM3MYmJmZw8DMzHAYmJkZDgMzM8NhYGZmOAzMzAyHgZmZ4TAwMzMcBmZmhsPAzMxwGJiZGQ4DMzPDYWBmZjgMzMwMh4GZmeEwMDMzqvsN5JGSHpS0UtIKSRdn/QBJSyWtyvuhWZekGyU1SnpK0vGlZU3N9qskTS3VPyjp6exzY/7uspmZ9ZJqtgy2AZdExNHAeGCGpLHATOD+iBgD3J+PAc4AxuRtOnAzFOEBzAJOpPiJy1ktAZJtppf6Tez+qpmZWbU6DIOIWB8Rj+f0VmAlMByYBMzLZvOAyTk9CZgfhUeAIZIOAU4HlkbExojYBCwFJua8/SLiVxERwPzSsszMrBd06piBpFHAccCjwMERsR6KwAAOymbDgbWlbk1Za6/eVKFuZma9pOowkDQY+CHwxYh4tb2mFWrRhXqlMUyX1CCpobm5uaMhm5lZlaoKA0m7UwTBbRFxd5Zfyl085P2GrDcBI0vdRwDrOqiPqFDfTkTMjoj6iKivq6urZuhmZlaFas4mEnALsDIivlGatQhoOSNoKnBPqX5+nlU0HtiSu5GWABMkDc0DxxOAJTlvq6Tx+Vznl5ZlZma9YGAVbU4CzgOelvRk1r4MXAsslDQNeAE4J+ctBs4EGoHXgQsAImKjpKuAZdnuyojYmNMXAnOBvYD78mZmfcSomT+p9RCsAx2GQUQ8TOX9+gCnVmgfwIw2ljUHmFOh3gAc29FYzMxsx/A3kM3MzGFgZmYOAzMzw2FgZmY4DMzMDIeBmZnhMDAzMxwGZmaGw8DMzHAYmJkZDgMzM8NhYGZmOAzMzAyHgZmZ4TAwMzMcBmZmhsPAzMxwGJiZGVWEgaQ5kjZIeqZUu1zSi5KezNuZpXmXSWqU9Jyk00v1iVlrlDSzVB8t6VFJqyTdKWlQT66gmZl1rJotg7nAxAr16yNiXN4WA0gaC0wBjsk+35I0QNIA4CbgDGAscG62BbgulzUG2ARM684KmZlZ53UYBhHxc2BjlcubBCyIiDcj4nmgETghb40RsToi3gIWAJMkCTgFuCv7zwMmd3IdzMysm7pzzOAiSU/lbqShWRsOrC21acpaW/UDgc0Rsa1VvSJJ0yU1SGpobm7uxtDNzKysq2FwM3AEMA5YD3w966rQNrpQrygiZkdEfUTU19XVdW7EZmbWpoFd6RQRL7VMS/oucG8+bAJGlpqOANbldKX6y8AQSQNz66Dc3szMekmXtgwkHVJ6+DdAy5lGi4ApkvaQNBoYAzwGLAPG5JlDgygOMi+KiAAeBM7O/lOBe7oyJjMz67oOtwwk3QGcDAyT1ATMAk6WNI5il84a4HMAEbFC0kLgWWAbMCMi3s7lXAQsAQYAcyJiRT7FpcACSVcDTwC39NjamZlZVToMg4g4t0K5zTfsiLgGuKZCfTGwuEJ9NcXZRmZmViP+BrKZmTkMzMzMYWBmZjgMzMwMh4GZmeEwMDMzHAZmZobDwMzMcBiYmRkOAzMzw2FgZmY4DMzMDIeBmZnhMDAzMxwGZmaGw8DMzHAYmJkZDgMzM6OKMJA0R9IGSc+UagdIWippVd4Pzbok3SipUdJTko4v9Zma7VdJmlqqf1DS09nnRknq6ZU0M7P2VbNlMBeY2Ko2E7g/IsYA9+djgDOAMXmbDtwMRXgAs4ATKX7veFZLgGSb6aV+rZ/LzMx2sA7DICJ+DmxsVZ4EzMvpecDkUn1+FB4Bhkg6BDgdWBoRGyNiE7AUmJjz9ouIX0VEAPNLyzIzs17S1WMGB0fEeoC8Pyjrw4G1pXZNWWuv3lShXpGk6ZIaJDU0Nzd3cehmZtZaTx9ArrS/P7pQrygiZkdEfUTU19XVdXGIZmbWWlfD4KXcxUPeb8h6EzCy1G4EsK6D+ogKdTMz60VdDYNFQMsZQVOBe0r18/OsovHAltyNtASYIGloHjieACzJeVsljc+ziM4vLcvMzHrJwI4aSLoDOBkYJqmJ4qyga4GFkqYBLwDnZPPFwJlAI/A6cAFARGyUdBWwLNtdGREtB6UvpDhjaS/gvryZmVkv6jAMIuLcNmadWqFtADPaWM4cYE6FegNwbEfjMDOzHcffQDYzM4eBmZk5DMzMDIeBmZnhMDAzMxwGZmaGw8DMzHAYmJkZDgMzM8NhYGZmOAzMzAyHgZmZ4TAwMzMcBmZmhsPAzMxwGJiZGQ4DMzOjil86M7O+adTMn9R6CLYT6daWgaQ1kp6W9KSkhqwdIGmppFV5PzTrknSjpEZJT0k6vrScqdl+laSp3VslMzPrrJ7YTfTRiBgXEfX5eCZwf0SMAe7PxwBnAGPyNh24GYrwAGYBJwInALNaAsTMzHrHjjhmMAmYl9PzgMml+vwoPAIMkXQIcDqwNCI2RsQmYCkwcQeMy8zM2tDdMAjgp5KWS5qetYMjYj1A3h+U9eHA2lLfpqy1Vd+OpOmSGiQ1NDc3d3PoZmbWorsHkE+KiHWSDgKWSvpNO21VoRbt1LcvRswGZgPU19dXbGNmZp3XrS2DiFiX9xuAH1Hs838pd/+Q9xuyeRMwstR9BLCunbqZmfWSLoeBpH0k7dsyDUwAngEWAS1nBE0F7snpRcD5eVbReGBL7kZaAkyQNDQPHE/ImpmZ9ZLu7CY6GPiRpJbl3B4R/yFpGbBQ0jTgBeCcbL8YOBNoBF4HLgCIiI2SrgKWZbsrI2JjN8ZlZmad1OUwiIjVwAcq1F8BTq1QD2BGG8uaA8zp6ljMzKx7fDkKMzNzGJiZmcPAzMxwGJiZGQ4DMzPDYWBmZjgMzMwMh4GZmeEwMDMzHAZmZobDwMzMcBiYmRkOAzMzw2FgZmY4DMzMjO7/BrKZ9ZBRM39S6yFYP+YtAzMzcxiYmdlOFAaSJkp6TlKjpJm1Ho+ZWX+yU4SBpAHATcAZwFjgXEljazsqM7P+Y2c5gHwC0BgRqwEkLQAmAc/WdFTWr/mArvUnO0sYDAfWlh43ASe2biRpOjA9H74m6bkuPt8w4OUu9t3Z9eV1g769fl63XVevrZ+u6/YiDq9U3FnCQBVqsV0hYjYwu9tPJjVERH13l7Mz6svrBn17/bxuu66+sH47xTEDii2BkaXHI4B1NRqLmVm/s7OEwTJgjKTRkgYBU4BFNR6TmVm/sVPsJoqIbZIuApYAA4A5EbFiBz5lt3c17cT68rpB314/r9uua5dfP0Vst2vezMz6mZ1lN5GZmdWQw8DMzPpXGPTlS15IGinpQUkrJa2QdHGtx9TTJA2Q9ISke2s9lp4kaYikuyT9Jv9+f1HrMfUkSf+Y/yafkXSHpD1rPaaukjRH0gZJz5RqB0haKmlV3g+t5Ri7qt+EQT+45MU24JKIOBoYD8zoY+sHcDGwstaD2AG+CfxHRLwX+AB9aB0lDQe+ANRHxLEUJ4hMqe2oumUuMLFVbSZwf0SMAe7Px7ucfhMGlC55ERFvAS2XvOgTImJ9RDye01sp3lCG13ZUPUfSCOAs4Hu1HktPkrQf8FfALQAR8VZEbK7tqHrcQGAvSQOBvdmFv0MUET8HNrYqTwLm5fQ8YHKvDqqH9KcwqHTJiz7zZlkmaRRwHPBobUfSo24A/gX4Y60H0sPeAzQD389dYN+TtE+tB9VTIuJF4N+BF4D1wJaI+GltR9XjDo6I9VB8KAMOqvF4uqQ/hUFVl7zY1UkaDPwQ+GJEvFrr8fQESR8DNkTE8lqPZQcYCBwP3BwRxwG/ZxfdzVBJ7j+fBIwGDgX2kfTJ2o7KKulPYdDnL3khaXeKILgtIu6u9Xh60EnAX0taQ7F77xRJP6jtkHpME9AUES1bcXdRhENfcRrwfEQ0R8QfgLuBD9d4TD3tJUmHAOT9hhqPp0v6Uxj06UteSBLFfueVEfGNWo+nJ0XEZRExIiJGUfzdHoiIPvHpMiJ+B6yVdFSWTqVvXbr9BWC8pL3z3+ip9KED5GkRMDWnpwL31HAsXbZTXI6iN9Tgkhe97STgPOBpSU9m7csRsbiGY7Lq/ANwW35IWQ1cUOPx9JiIeFTSXcDjFGe8PcEufOkGSXcAJwPDJDUBs4BrgYWSplGE3zm1G2HX+XIUZmbWr3YTmZlZGxwGZmbmMDAzM4eBmZnhMDAzMxwGZmaGw8DMzID/D1OLRUY4inWuAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "trusted": true,
        "scrolled": true
      },
      "cell_type": "code",
      "source": "n2, bin2, patch2 = plt.hist(fair_heads, bins = np.arange(0,12))\nplt.title(\"Number of Heads for Fair Coin\")\nplt.show()",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": "<Figure size 432x288 with 1 Axes>",
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "biased_heads.count(9), fair_heads.count(9)",
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 7,
          "data": {
            "text/plain": "(38634, 8810)"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "b9 = biased_heads.count(9)\nf9 = fair_heads.count(9)\n\nb9/(b9+f9)",
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
            "text/plain": "0.8143073939802715"
          },
          "metadata": {}
        }
      ]
    },
    {
      "metadata": {},
      "cell_type": "markdown",
      "source": "The chances that the coin flipped is a biased one = 81.4%"
    },
    {
      "metadata": {
        "trusted": true
      },
      "cell_type": "code",
      "source": "",
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3",
      "language": "python"
    },
    "language_info": {
      "name": "python",
      "version": "3.6.9",
      "mimetype": "text/x-python",
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "pygments_lexer": "ipython3",
      "nbconvert_exporter": "python",
      "file_extension": ".py"
    },
    "gist": {
      "id": "",
      "data": {
        "description": "some-cool-stuff/coin_sim.ipynb",
        "public": true
      }
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}