7_Getting_Sum_of_dice_rolls.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/Getting_Sum_of_dice_rolls.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: What is the probability of rolling a sum of 7 on a pair of fair six-sided dice?\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "# 2. Standard Solution:\n",
        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)\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6w6v56sG8JM5"
      },
      "source": [
        "# 3. Programing Solution"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.1 Using a Formula to find the pairs that sum 7"
      ],
      "metadata": {
        "id": "mhg8t65YXwE4"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "DfJ6ZrpE5ENT",
        "outputId": "f44d0712-327d-41fa-90cb-63b95bd7ea90",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6\n"
          ]
        }
      ],
      "source": [
        "def get_number_of_pairs_that_sum_target(target:int, a=1, b=6):\n",
        "  return max(0,min(target-a,b)-max(1,target-b)) + 1\n",
        "\n",
        "print(get_number_of_pairs_that_sum_target(7))"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.2 Using bruteforce to find the pairs"
      ],
      "metadata": {
        "id": "n0D7am6WX-Mq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def find_by_brute_force(target:int=7):\n",
        "  count = 0\n",
        "  for x in range(1,7):\n",
        "    for y in range(1,7):\n",
        "      if x + y == target:\n",
        "        count += 1\n",
        "  return count\n",
        "\n",
        "print(find_by_brute_force(7))"
      ],
      "metadata": {
        "id": "U99UswoVXibF",
        "outputId": "10c4a5f2-767b-45b3-dab9-bb7e24e0659e",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.3 Testing Formula vs Bruteforce"
      ],
      "metadata": {
        "id": "vZ8fUHO-YvcJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "assert get_number_of_pairs_that_sum_target(7) == find_by_brute_force(7), f'Results are different, please review functions {get_number_of_pairs_that_sum_target(7)} vs { find_by_brute_force(7)}'\n",
        "assert get_number_of_pairs_that_sum_target(8) == find_by_brute_force(8), f'Results are different, please review functions {get_number_of_pairs_that_sum_target(8)} vs { find_by_brute_force(8)}'\n",
        "print('Both algorithms give the same result')"
      ],
      "metadata": {
        "id": "xKtQMIxXYqci",
        "outputId": "d2db3ee1-decc-40cd-9e37-8510d89e0f3d",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Both algorithms give the same result\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### 3.4 Now that we have the number of pairs, we calculate:"
      ],
      "metadata": {
        "id": "aDmd_Li-aqvy"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def probability_to_obtain_sum_in_six_sided_dice(target:int = 7):\n",
        "  all_probabilities = 6 ** 2\n",
        "  sum_target_probability = get_number_of_pairs_that_sum_target(target = 7)\n",
        "  return sum_target_probability / all_probabilities"
      ],
      "metadata": {
        "id": "ZudMIA_HZIuq"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# 4. Testing"
      ],
      "metadata": {
        "id": "_NlP3fvScPfT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "prob = probability_to_obtain_sum_in_six_sided_dice(7)\n",
        "assert prob == 6/36, f'Incorrect, The probabilities for obtainig 7 is given by 6/36, returned: {prob}'\n",
        "\n",
        "print('Probability computed correctly')"
      ],
      "metadata": {
        "id": "G7qxI5TOcSvy"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "ql0unWQDcf5u"
      },
      "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
}