14_Probability_not_sent_to_prison.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/14_Probability_not_sent_to_prison.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 study of pleas and prison sentences, it is found that 45% of the subjects studied were sent to prison. Among those sent to prison, 40% chose to plead guilty. Among those not sent to prison, 55% chose to plead guilty.\n",
        "\n",
        "## a. If one of the study subjects is randomly selected, find the probability of getting someone who was not sent to prison.\n",
        "\n",
        "## b. If a study subject is randomly selected and it is then found that the subject entered a guilty plead, find the probability that this person was not sent to prison.\n",
        "\n",
        "link: https://math.oxford.emory.edu/site/math117/probSetBayesTheorem/\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "# 2. Standard Solution:\n",
        "\n",
        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      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6w6v56sG8JM5"
      },
      "source": [
        "# 3. Programing Solution"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.1 Response A: Probability not sent to prison"
      ],
      "metadata": {
        "id": "2tLeWByAda8V"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "DfJ6ZrpE5ENT",
        "outputId": "1e862aef-c4d5-43f6-fc12-de9e243484bc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Result: Probabiliy not sent to prison: 0.55\n"
          ]
        }
      ],
      "source": [
        "\n",
        "def probability_not_sent_to_prison(\n",
        "    sent_to_prison = 0.45,\n",
        "plead_guilty_given_sent_to_prison = 0.40,\n",
        "plead_guilty_given_not_sent_to_prison = 0.55,\n",
        "):\n",
        "  return 1 - sent_to_prison\n",
        "\n",
        "print(f'Result: Probabiliy not sent to prison: {probability_not_sent_to_prison()}')"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "def probability_not_sent_to_prison_given_entered_guilty_plead(\n",
        "    sent_to_prison = 0.45,\n",
        "    plead_guilty_given_sent_to_prison = 0.40,\n",
        "    plead_guilty_given_not_sent_to_prison = 0.55,):\n",
        "  return (1 - sent_to_prison) * plead_guilty_given_not_sent_to_prison/( (1 - sent_to_prison) * plead_guilty_given_not_sent_to_prison\n",
        "                                                                       + sent_to_prison * plead_guilty_given_sent_to_prison)\n",
        "print(f'Result: Probability not sent to prison given entered guilty plead {probability_not_sent_to_prison_given_entered_guilty_plead()}')"
      ],
      "metadata": {
        "id": "DTeN-8A1bB6P",
        "outputId": "3410bfbb-ff19-4569-9294-97c2068edbbe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Result: Probability not sent to prison given entered guilty plead 0.6269430051813472\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ICIlgyC4dAZ9"
      },
      "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",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.12.0"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}