4_Coin_Tosses.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/4_Coin_Tosses.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: Consider tossing a fair coin three times. What is the probability of getting heads on all three tosses? Remember, each toss is independent.\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "# 2. Standard Solution:\n",
        "\n",
        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)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6w6v56sG8JM5"
      },
      "source": [
        "# 3. Programing Solution"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "DfJ6ZrpE5ENT"
      },
      "outputs": [],
      "source": [
        "# P(HHH) = P(H)**n_tosses\n",
        "def same_face_probability(n_tosses: int=3) -> float:\n",
        "  prob_face = 1/2\n",
        "  prob_all_same_face = prob_face**n_tosses\n",
        "  return prob_all_same_face\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "4. Testing"
      ],
      "metadata": {
        "id": "vdKy2-qJKWmz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "assert same_face_probability(n_tosses=3) == 1/8, f'Incorrect, the probability of getting same face 3 times is {1/8}, returned: {same_face_probability(3)}'\n",
        "assert same_face_probability(n_tosses=4) == 1/16, f'Incorrect, the probability of getting same face 3 times is {1/16}, returned: {same_face_probability(4)}'\n",
        "print('Computed same face probability correctly')"
      ],
      "metadata": {
        "id": "sapVcGgUJhZW",
        "outputId": "6f9eea4b-7e41-4fbb-ad39-61c692052a5c",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Computed same face probability correctly\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "yvXkEmcFKsNM"
      },
      "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
}