13_Transportation_and_being_late.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/gmdeorozco/Probability-Problems-Python-Solutions/blob/main/13_Transportation_and_being_late.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3_Nw-GnY5lRT"
      },
      "source": [
        "# 1. Problem: A person uses his car 30% of the time, walks 30% of the time and rides the bus 40% of the time as he goes to work. He is late 10% of the time when he walks; he is late 3% of the time when he drives; and he is late 7% of the time he takes the bus. a. -> What is the probability he took the bus if he was late?  b.-> What is the probability he walked if he is on time?\n",
        "link:  https://math.oxford.emory.edu/site/math117/probSetBayesTheorem/\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "# 2. Standard Solution:\n",
        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xJ5gXMcIKl0AUAcheepOBzT79r8+JYryDS7i6t7W0dYWjliAkkcrz8zggALjOP4jQ7Xsha2uR3GteIbW2uZ59K0hYrX/XMNUmOzgHtbehBqKLxFrk27bpmkKyhSySanOjAMcK21rUHBPGenBqXV4by60vULO3tHunubqOOcRMi4jKReZ95h/DuAplxaXH2LX7u6tmiN3biC3SV1Mv3SoXKkgAs3AHcknrRoVYufa/FP/QH0f/wby/8AyNWdquo6s3lWOreH9FuBcElIXvZ5g+OvAtSOK3LmG8a8tGjkj2qzZzETt+Q9TuqlPZX174sjmcXFtbWtmyR3EZixI7spb5TuIwEHOO55pdRLa5n3Gp6vd6Y0P9maK1tNAzAw6tKQEHBIxbcY/wA9Kqma6vZBLdeG/Dt1cyW/mtI91KXkjH8XNrkj0+vvW3a6dDZajdWNvF5cDWEccCZzkBpN3XqcupJP96svSPD+pQ3OjSXqKuzSza3mHB24MW1B652tnty3qKas3/Xn/wAAHpt/W3/BJobzxDeX0Vwmk6STHDmKNtTmTAY8tg22f4ce3PrUdxqGqWOso8vh7RV1C4jOJY72ZpHRSM5ZbQnAyOp4yK2rxJZdehFo6xypZTAyMu4Rlmj2ErkZ5Vu4+6aqvY3t74rlnmW4tbaCzEMM6NHiVmbMnHLD7qdh0NL/AIP6h0/r+vMoi61u/vI5odL0OcT23zKurSOksRPBP+jY6k49ct+FS1N41lK2leHPD9qpH2Yyw3ksePm27P8Aj1HRhgjsRzW3aQLpF5ewWNozLFawi2gjIGUUMAoLEDg5zk/xe9VNKjvrXQLSzvLCS2MXktNJI6HzJmlUtt2seMlic46j3p6dP63D1M83E32p7g+GvDnn/aQjSm7l3GbsM/ZOW6e/SrkOo+IG1KaY6VpRlLC2G/Up1C4ydoJtecnJyODwKivdB1OWa+kgiQ/8TeC7tVZhggeVvc+mNre/X1FbeqQCLTLe3jy7m6g25PzMRKrMfrgMx+hoVrL+ui/4KDW/9d3/AMBkP2vxTnH9j6Pn/sLy/wDyNVK58Q67aXgtZ9K0pZjGZcDUbhgEBwWJFrgAdyelbEkV4dXhdZItghkGfJJxlkwCd3Xj9Kzxpl1qPiHUpr1Lm1tWgjtYtrx4mQbi5yCWXJbH8J4/JANj1bxFM2IdK0aT92Jcpq0rAqehBFtznBxVa08T61ehPs+maSfMz5e/UrhPMx127rUbiMHgZq5Gs+nR61FptoZZ02NaW6FV+TyVVACxAA3I3fsajsdJnePRIJbeS0t9IAcmVkLSuIjGPukjHzMSSRzjjrT0C2mpLFf+JpoUli0jRnjdQysNXlwQe/8Ax7VStfE2s3bqsOm6QCztGvmalPGHdc7lBa1GSNrZA6YPpWlpn2qHSFngXzYyJpI7dQN8m6QtGQxYADaeh9evFZkHh2ceDUW7Ez6jFaSukTlMRXDo28rt6klm5JPWjTUaV9CaXX9ehtoZ5NK0kRzkCIjU5zvJ6AAWucnt61M2p+JUMgOj6TmJBIwGqTEhTnHAtufungc0moNcXWoaPPZ6fPdWNuGud8LxjLGMqi4ZwejsfwFGovqUljqP2S0ZtQmsI1SJHQeW7eZ1JYDjPrzjik9nYS1tcq2vifWbyJZLfTdJKvEZo92pTqZEABLKDajcORyM9R610dhLcT2MUt7HBFM4yVt5jKmM8YcqpORg9B+PWsmGwdrzT55YGsLLSoXWOOVk3MSoUH5SQFC578k9sc39CR4tAsUkVkYQL8rdVGOAfoKbt0Er21L9FFFSMKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACk2ru3YG4jGcc4paKAEZVcYdQwyDgjPI5FLRRQAUiqEUKgCqBgADAFLRQAgVVJKgAscnA6np/ShlVsblBwcjI6GlooAKKKKAEKgsCQCV6HHSloooAQKoYsFALdSB1paKKAEKqWDEDcOAccihlVxhgGGQcEdxzS0UAFIVUsGKgsvQ45FLRQAUUUUAJtXcGwNwGAcc4oZVdSrgMrDBBGQRS0UAFFFFACKqoMKAoznAFG1QxYAbiACcckf5JpaKAEZVdSrqGU9QRkGloooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAZNNHbwvNPIkUUalnd2AVQOSST0FOBDKCpBBGQR3rI8Xf8AIla3/wBg+f8A9FtWBoup6fba5AdN1qS6sjZk6i1zetKkE25BGDvOInYs48sben3eBTSuD0S/rt/mdl9pgN0bUTR/aAgkMW8bwpOA2OuMgjPtUTanYLaxXLX1sIJm2xymVdrn0Bzgng/lXM+OHuNNubDVLBSZ5Vl0zgcAzAeWT9JEQZ/2jWPaacbPV5vDqKRZaHDPexEqcESx7Yxk+haf/vkUvs3/AK0/4Fh21S/r+rno0UqTRJLC6yRuoZHQ5DA9CD3FJNPFbqrTypErMEUuwALE4A57knAFedW1w2g2Vhi+1L7PceHWuLjZP5jKyeSA0YkOyMgSN0AXoT0rMku7a9tbyK81P/Qba+sLiN4ddmuERGl2yP57FWKjA7lVYcEGtHC0rf1vYhSvG/8AW1z1eS4hiliilmjSSYkRozAFyBkgDvwCakrn9Zu3h1LRPslzKIZPPJMRaTzAIGKnA+/yAQOcmsnwRepdXVzai8e+YWytNcRapLcozZI+dHANvIeT5a8DkfwiosO+lzr1vrR1jZbqFhLIYoyJB87jOVHqRtbj2PpU9eZ6dZWUmm6Vp8F7ceYviC4S5Vb6RpYuLnC5LFoyVA6YJznqc0XWo38FvHazXmNLg1C8gee81WW0+6w8pHuVVn6FsZI3bQCT0Lt0/rp/mP8Ar8/8j0yiuJur28T4b2U93qEqyG6t0e6t3kDGI3KrkMyqzZTq20buvINUWuhLPNbaFrF5c6O99Yot1HfPNh2ciWNJiSSNoTI3HBY9Oxy3dvO35f5iv7vN8z0SmQzxXCs0EqSqrMjFGBAYHBHHcEEEVwl5dfZLy7hGp3cetW9zHFpli15IfOhwmD5ZY+aCC+6RgxHzcjbxTtLq2gnl/s/VLj+3P7clWOwW6fa8RuWD5gztKbC5LlTgj7wxgCV7f12/z1G9F/Xn/keksyohd2CqoySTgAVGbq3WzN208QthH5pmLjYExndu6YxzmvNhrqyeIh5GoSGO4+1wXCXGpmSQNscqj24Hlw8p8uDuIHIyWqGK/jt/DNufDur3VxcDRJm1CP7Y8n2Yi3yjbScQuHAAA25BPBxwkrr+vP8AyH9pR/rp/mel/wBo2WcfbLfPmLFjzV++wBVevUgggdwRU0M8VzEJbeVJYySA6MGBIODyPQgiuHEso1O8VJpY/P1m0jkMcjKWU2seRkHNUNMul8P+GYNT0ua5vGsb24gvrL7bJKfnkZVBRmO1gwjPQcMx7nLt/XyX+ZPb0uejzTxW6B7iVIlLKgZ2CgsxwBz3JIAHqafXJa3YT23gmxs7y6mluTe2fnT+YSxdrlCxBOcDJOB2GAOlYmp3l9p09/p8F3J/ZdtqcaSy3mpzRGONrYPta5w7opkI5z3C5ANK39fd/mUekUVxtk+pXPw+upre7M1zbu81nJBcSyb1Rt6J5rKplU427sEMD1PWsvStX1S/1aFZZrz7Leb9bjZGPFsFZUhUfXyWK9DuNFv6/r5/cL+v6/D7z0OeeK2haa5lSGJBlnkYKqj3JoinimMghlSQxvscIwOxuuD6Hkce9eStrK3NnqcUGoGe1utLaRRJqpvHeRXX7wxsikCt80cZKjI7AVsLd3tv4mvvtRaDRzqkgSaG4aMvdeXH5aykYxGeQOcFiARjAL5bb9n+Dt/w3yJv+f6XPRajNxCLkW5mjE7IXEW4bioIBbHXGSBn3rzDTdW1xrWeWzvUl1L+z5mu4I7+a7lWYAEEwNEEt2DbsJkA9AGxxs6BJpMnj6A6Hqs2pQ/2VLvd7xrkK3mx/wAbEkHplM8cHAzy+XW39df8ht6X/rp/mddNq+m267p9QtYl8/7Pl5lA83/nnyfvf7PWrIniNw0AlQzKodoww3BSSASOuCQefY1wvkf2h4s057ue6Yw6veJHtupECqsWQMKwGMjp6ZHQkVN4ktPO8Qa3cLc3dvJa6HHLEba4eL5w05BO0jdjHQ5U55B4qNFFN9r/AIXKSbbS6afjY7eo2uIVuEt2ljE0ilkjLDcwGMkDqQMj8xXmupavq0uoM0t7Ba3Jjt308PqM0JkyilittHGwuMuWBHJGMYXqej8U3lzBqiRwX01oraTdMXiR5AjB4QH2LySNx5xwCTVONvx/BCj7x1dFcl4TvzcaZqf9nt9oaE/u3TVH1CB3KZwkzgNnpuXoOMdTWDJqZXRZpNI1i8ub06TcSaorXTu1tKIsqSpJ8hw+QEXb34+UYVtWEfet5npdQG/tAoY3UABl8gHzBzJnGz/ezxjrXO6Kklj4skslu7ueGbTY7lxc3Dy/vd7AsNxO3I/hXC8DAFY2lG3055LWxvp/tI8Q7LiFr2SRljLOV3KzEgMOc/xYyc0W1t/W6Qr+7f8Ara56FRXnunWc10NAafVdVb+0nuEugL+VQ6qGZQMH5MFQMptJGQScnObJq+ovp9kmoX6xWawzxxXFzq8tiXlSd0GZERjI4RV+Vj82ScMegM9IbWNNTVF0x9QtFv3GVtDOolYYzkJnPQE9KuVxK6dPd2ukaVttUmuzHqmoXTyMsxljaNiUicB8s2BkhQg4x0Wu2ptW/r+v61FcKKKKkYUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAQXllb38KxXcfmIsiSgbiMMjBlPHoQDU9FFABRRRQAUUUUAFVL3S7TUZbd7yNpP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)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6w6v56sG8JM5"
      },
      "source": [
        "# 3. Programing Solution"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.1 Data"
      ],
      "metadata": {
        "id": "d4IvEb3v1wpa"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 12,
      "metadata": {
        "id": "DfJ6ZrpE5ENT"
      },
      "outputs": [],
      "source": [
        "#Data\n",
        "\n",
        "uses_car = 0.30\n",
        "uses_bus = 0.40\n",
        "walks = 0.30\n",
        "\n",
        "is_late_when_walks = 0.10\n",
        "is_late_when_car = 0.03\n",
        "is_late_when_bus = 0.07\n",
        "\n",
        "# Questions\n",
        "# What is the probability he took the bus if he was late?\n",
        "# What is the probability he walked if he is on time?"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.2 What is the probability he took the bus if he was late?"
      ],
      "metadata": {
        "id": "NWsgURPU1tQT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def prob_took_the_bus_given_he_is_late(\n",
        "    uses_car = 0.30,\n",
        "    uses_bus = 0.40,\n",
        "    walks = 0.30,\n",
        "\n",
        "    is_late_when_walks = 0.10,\n",
        "    is_late_when_car = 0.03,\n",
        "    is_late_when_bus = 0.07,):\n",
        "  return uses_bus * is_late_when_bus/(uses_car*is_late_when_car + walks * is_late_when_walks + uses_bus * is_late_when_bus)\n",
        "\n",
        "print(f'Result: The probability he took the bus if he was late is -> {prob_took_the_bus_given_he_is_late()}')\n",
        ""
      ],
      "metadata": {
        "id": "u-17CLatyaGl",
        "outputId": "b9e3344c-701c-4d0c-8e98-55a537195c55",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Result: The probability he took the bus if he was late is -> 0.41791044776119407\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.3 What is the probability he walked if he is on time?"
      ],
      "metadata": {
        "id": "UArLY6T714c6"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def prob_walked_given_he_is_on_time(\n",
        "    uses_car = 0.30,\n",
        "    uses_bus = 0.40,\n",
        "    walks = 0.30,\n",
        "\n",
        "    is_late_when_walks = 0.10,\n",
        "    is_late_when_car = 0.03,\n",
        "    is_late_when_bus = 0.07,):\n",
        "\n",
        "  return walks * (1-is_late_when_walks) / (uses_car*(1-is_late_when_car) + walks * (1-is_late_when_walks) + uses_bus * (1-is_late_when_bus))\n",
        "\n",
        "print(f'Result: The probability he walked if he is on time is -> {prob_walked_given_he_is_on_time()}')\n"
      ],
      "metadata": {
        "id": "x1pGRdVoyrMy",
        "outputId": "acdd67df-f203-4493-85a0-51cb38720296",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Result: The probability he walked if he is on time is -> 0.2893890675241158\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "NMRBz1Ie094E"
      },
      "execution_count": 14,
      "outputs": []
    }
  ],
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "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": "3.12.0"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}