notebooks/basic_concepts/geometric_probability.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "6f45f93d-e8d9-4ffc-84be-4764f263a75b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import quad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "1ff3beb8-2245-4ed5-bdc7-45add3c0a712",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_probability(r):\n",
    "    \"\"\"\n",
    "    Calculate the probability that a randomly chosen point inside the square\n",
    "    is at a distance less than r from the bottom left corner (0,0).\n",
    "    \"\"\"\n",
    "    if r < 1:\n",
    "        # When the circle is completely within the square\n",
    "        probability = (np.pi * r**2) / 4\n",
    "    elif r == np.sqrt(2):\n",
    "        # When the circle exactly covers the square\n",
    "        probability = 1\n",
    "    else:\n",
    "        # When the circle extends outside the square\n",
    "        # Integral from 0 to 1 for the area within the square\n",
    "        area_within_square, _ = quad(lambda x: np.sqrt(r**2 - x**2), 0, 1)\n",
    "        probability = area_within_square\n",
    "\n",
    "    return probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f89d3ee2-3b52-4320-a3dc-84a209f86ca1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_square_and_circle(r):\n",
    "    \"\"\"\n",
    "    Plot the square and the quarter circle to visualize the problem.\n",
    "    \"\"\"\n",
    "    # Create a figure\n",
    "    fig, ax = plt.subplots()\n",
    "\n",
    "    # Plot square\n",
    "    square = plt.Rectangle((0, 0), 1, 1, edgecolor='black', facecolor='none')\n",
    "    ax.add_patch(square)\n",
    "\n",
    "    # Plot quarter circle\n",
    "    theta = np.linspace(0, np.pi/2, 100)\n",
    "    x = r * np.cos(theta)\n",
    "    y = r * np.sin(theta)\n",
    "    ax.plot(x, y, color='red')\n",
    "\n",
    "    # Setting the limits of the plot\n",
    "    ax.set_xlim(0, max(1.1*r, 1))\n",
    "    ax.set_ylim(0, max(1.1*r, 1))\n",
    "    ax.set_aspect('equal', adjustable='box')\n",
    "    ax.set_xlabel('X')\n",
    "    ax.set_ylabel('Y')\n",
    "    ax.set_title(f'Quarter Circle with radius {r} in a Square')\n",
    "\n",
    "    return fig, ax"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3604e38-a765-4a3e-a3f8-8e6104f1737c",
   "metadata": {},
   "source": [
    "## Display Probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "963ca86e-a07d-4dd9-bc7d-02f94cc4f745",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5026548245743669"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r = 0.8\n",
    "probability = calculate_probability(r)\n",
    "plot_square_and_circle(r)\n",
    "probability"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}