14 Probability.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6fdc034c-f93a-4447-8478-304abf0c61d5",
   "metadata": {},
   "source": [
    "##### Theoritical Probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "819fd3c4-9a42-4f2a-91ef-7b4cb1467ae1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def coin_flip_probability():\n",
    "  heads_probability = 1 / 2\n",
    "  return heads_probability\n",
    "\n",
    "def rolling_dice_probability(number):\n",
    "  if number not in range(1, 7):\n",
    "    raise ValueError(\"Number must be between 1 and 6\")\n",
    "  probability = 1 / 6\n",
    "  return probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0eb6e26f-83ec-477e-b119-d0d7ff4f651b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of heads in a coin flip: 0.5\n",
      "Probability of rolling a 4 on a die: 0.16666666666666666\n"
     ]
    }
   ],
   "source": [
    "# Example usage\n",
    "coin_flip_result = coin_flip_probability()\n",
    "dice_roll_result = rolling_dice_probability(4)\n",
    "\n",
    "print(\"Probability of heads in a coin flip:\", coin_flip_result)\n",
    "print(\"Probability of rolling a 4 on a die:\", dice_roll_result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfa16db0-11b1-4209-9053-41dce3f3af08",
   "metadata": {},
   "source": [
    "##### Experimental Probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "64199744-2fe0-4b53-aa03-593885c73cd8",
   "metadata": {},
   "outputs": [],
   "source": [
    "import random\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "3a8d1578-7253-4e0f-b28a-4ee10a98cfe5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def simulate_coin_flips(num_flips):\n",
    "  results = []\n",
    "  for _ in range(num_flips):\n",
    "    flip = random.choice([\"heads\", \"tails\"])\n",
    "    results.append(flip)\n",
    "  return results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "308d40bf-94f5-428c-824a-789e66930a85",
   "metadata": {},
   "outputs": [],
   "source": [
    "simulate_coin_flips(100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "f3937db2-cbf2-4529-a689-9fdf3e1827e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tails    55\n",
       "heads    45\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(simulate_coin_flips(100)).value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "876f1f57-9ea7-4ae0-a9b1-c1e8245b39b4",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculate_experimental_probability(results, event):\n",
    "  event_count = results.count(event)\n",
    "  total_flips = len(results)\n",
    "  probability = event_count / total_flips\n",
    "  return probability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "8c46b022-f4cc-4240-b4f0-a90418959c0d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of flips: 1000\n",
      "Heads probability: 0.4960\n",
      "Tails probability: 0.5040\n"
     ]
    }
   ],
   "source": [
    "# Example usage\n",
    "num_flips = 1000\n",
    "simulation_results = simulate_coin_flips(num_flips)\n",
    "\n",
    "heads_probability = calculate_experimental_probability(simulation_results, \"heads\")\n",
    "tails_probability = calculate_experimental_probability(simulation_results, \"tails\")\n",
    "\n",
    "print(f\"Number of flips: {num_flips}\")\n",
    "print(f\"Heads probability: {heads_probability:.4f}\")\n",
    "print(f\"Tails probability: {tails_probability:.4f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "567db71d-7c45-4250-b364-bcc4b6385783",
   "metadata": {},
   "source": [
    "##### Linear Growth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "95fac53e-9a0a-46de-a6a0-23bd8b7a3964",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "487b3fd8-6df8-4a5e-935d-bdcd7d70798a",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(0,10,0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "a30ec9b8-c50b-4e83-900a-f959b30285e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.  , 0.25, 0.5 , 0.75, 1.  , 1.25, 1.5 , 1.75, 2.  , 2.25, 2.5 ,\n",
       "       2.75, 3.  , 3.25, 3.5 , 3.75, 4.  , 4.25, 4.5 , 4.75, 5.  , 5.25,\n",
       "       5.5 , 5.75, 6.  , 6.25, 6.5 , 6.75, 7.  , 7.25, 7.5 , 7.75, 8.  ,\n",
       "       8.25, 8.5 , 8.75, 9.  , 9.25, 9.5 , 9.75])"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d09b2826-770d-4bb1-bb27-c1fec043bacc",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x * 0.3474765 + 15.005472"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "f3b9c6c0-cff4-49d9-a8f4-ac8ea00d8b3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15.005472  , 15.09234112, 15.17921025, 15.26607937, 15.3529485 ,\n",
       "       15.43981762, 15.52668675, 15.61355587, 15.700425  , 15.78729412,\n",
       "       15.87416325, 15.96103237, 16.0479015 , 16.13477062, 16.22163975,\n",
       "       16.30850888, 16.395378  , 16.48224713, 16.56911625, 16.65598538,\n",
       "       16.7428545 , 16.82972362, 16.91659275, 17.00346187, 17.090331  ,\n",
       "       17.17720012, 17.26406925, 17.35093837, 17.4378075 , 17.52467662,\n",
       "       17.61154575, 17.69841487, 17.785284  , 17.87215313, 17.95902225,\n",
       "       18.04589138, 18.1327605 , 18.21962962, 18.30649875, 18.39336787])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "e129a4a0-8ba9-4eab-b001-d84b185b6787",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "4408f97f-7841-4e66-9183-f2d9b9127db5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7e7e46ef2a40>]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "ccc060bd-2772-4f1d-ba5f-bea6ab661da9",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x * -0.3474765 + 15.005472"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "11738751-83cb-41b4-af64-c0d1ba8f9170",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([15.005472  , 14.91860287, 14.83173375, 14.74486462, 14.6579955 ,\n",
       "       14.57112637, 14.48425725, 14.39738812, 14.310519  , 14.22364987,\n",
       "       14.13678075, 14.04991163, 13.9630425 , 13.87617337, 13.78930425,\n",
       "       13.70243512, 13.615566  , 13.52869687, 13.44182775, 13.35495862,\n",
       "       13.2680895 , 13.18122037, 13.09435125, 13.00748212, 12.920613  ,\n",
       "       12.83374387, 12.74687475, 12.66000563, 12.5731365 , 12.48626737,\n",
       "       12.39939825, 12.31252912, 12.22566   , 12.13879087, 12.05192175,\n",
       "       11.96505262, 11.8781835 , 11.79131437, 11.70444525, 11.61757612])"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "c1c5d118-f6ee-440f-9f99-c9b1cfa26f12",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7e7e44defee0>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "7546729d-2ab5-463f-903b-43416f7d19bf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1., -1.],\n",
       "       [-1.,  1.]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4112c594-4928-4ffb-b149-06463096e406",
   "metadata": {},
   "source": [
    "##### Exponential / Polynomial Growth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "759340c4-9f10-4c31-aa00-cefc1fed7b35",
   "metadata": {},
   "outputs": [],
   "source": [
    "y = x ** 2 + 5.623"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "e4d118e0-b7b8-48e1-a353-ed87aa730bc3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7e7e44cfae30>]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a7b40d62-91a6-44ea-8552-93ee0d5a6a66",
   "metadata": {},
   "source": [
    "##### Logarithmic Growth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "1e26927c-0518-4334-b28e-81dacc420c08",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/tmp/ipykernel_371681/2742365056.py:1: RuntimeWarning: divide by zero encountered in log\n",
      "  plt.plot(x, np.log(x))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7e7e44d54f70>]"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, np.log(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c70825ee-5302-4d54-8a5b-9837180a0aaf",
   "metadata": {},
   "source": [
    "##### Logistic Growth"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "0ab28d2a-dcae-4363-b913-91da64311727",
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.arange(-5,5,0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "79ce90c5-b81a-4520-8640-796286b0437d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-5.  , -4.75, -4.5 , -4.25, -4.  , -3.75, -3.5 , -3.25, -3.  ,\n",
       "       -2.75, -2.5 , -2.25, -2.  , -1.75, -1.5 , -1.25, -1.  , -0.75,\n",
       "       -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ,  1.25,  1.5 ,\n",
       "        1.75,  2.  ,  2.25,  2.5 ,  2.75,  3.  ,  3.25,  3.5 ,  3.75,\n",
       "        4.  ,  4.25,  4.5 ,  4.75])"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "0f73a0e5-efbf-4088-93a0-8da2ea723695",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7e7e44c1a560>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, (1 / (1 + np.exp(-x))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dae77649-ff52-4769-9708-981e72e723e3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}