11_Correctly_Diagnosed_Sick.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/11_Correctly_Diagnosed_Sick.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: In a population of 1 000 000 individuals, a certain condition affects 1 of each 10 000 people. If a diagnostic test is 99% accurate, what is the probability that a randomly chosen person is correctly diagnosed as having the condition?\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "# 2. Standard Solution:\n",
        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        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6w6v56sG8JM5"
      },
      "source": [
        "# 3. Programing Solution"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "DfJ6ZrpE5ENT",
        "outputId": "bee8ee93-5f3d-4f7e-fd91-88a44cd4963a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.00980392156862745\n"
          ]
        }
      ],
      "source": [
        "# P(Being sick|Diagnosed sick) = [ P(Diagnosed sick | Being sick)*P(Being sick) ] / P(Diagnosed sick)\n",
        "def prob_correctly_dignosed_sick(prob_affected: float=1/10000, prob_accuracy: float=0.99, population:int=1000000) -> float:\n",
        "  people_sick = population * prob_affected\n",
        "  people_healthy = population - people_sick\n",
        "\n",
        "  people_sick_diagnosed_sick = prob_accuracy * people_sick\n",
        "  # people_sick_diagnosed_healthy = people_sick - prob_accuracy * people_sick\n",
        "\n",
        "  # people_healthy_diagnosed_healthy = prob_accuracy * people_healthy\n",
        "  people_healthy_diagnosed_sick = people_healthy - (prob_accuracy * people_healthy)\n",
        "\n",
        "  prob_being_sick_given_diagnosed_sick = people_sick_diagnosed_sick / ( people_healthy_diagnosed_sick + people_sick_diagnosed_sick)\n",
        "\n",
        "  return prob_being_sick_given_diagnosed_sick\n",
        "\n",
        "print(prob_correctly_dignosed_sick(1/10000,0.99,1000000))\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "0ghNVy6fzk9z"
      },
      "execution_count": null,
      "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",
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