Random_number_sensors.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#  выбор темы картинок на Ваш вкус. Необязательная строчка.\n",
    "#  matplotlib.style.use('ggplot')\n",
    "#  Эта строчка нужна для того, чтобы картинки отображались в ячейках\n",
    "%matplotlib inline\n",
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  Задаем зерно датчика a, \n",
    "#  опция version=2 требует преобразовать а в целое число, если требуется\n",
    "random.seed(a=12345, version=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Лабораторная 1."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "КОРШУНОВ,ФОСС СБОРНИК ЗАДАЧ ПО теории вероятностей 2 издание. n 27.\n",
    "Некто написал n адресатам письма, в каждый конверт вложил по одному письму и затем наудачу написал на каждом конверте один из n адресов. Найти вероятность того, что хотя бы одно письмо попало по назначению."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n=10\n",
      "500: 0.622\n",
      "1000: 0.641\n",
      "2000: 0.6165\n",
      "4000: 0.627\n",
      "8000: 0.6285\n",
      "16000: 0.62625\n",
      "32000: 0.6371875\n",
      "64000: 0.634109375\n",
      "128000: 0.632140625\n",
      "256000: 0.6329375\n",
      "n=50\n",
      "500: 0.67\n",
      "1000: 0.637\n",
      "2000: 0.6415\n",
      "4000: 0.6405\n",
      "8000: 0.62925\n",
      "16000: 0.6303125\n",
      "32000: 0.6325\n",
      "64000: 0.632515625\n",
      "n=100\n",
      "500: 0.65\n",
      "1000: 0.619\n",
      "2000: 0.633\n",
      "4000: 0.6335\n",
      "n=1000\n",
      "500: 0.626\n",
      "1000: 0.659\n",
      "2000: 0.6335\n",
      "4000: 0.63575\n",
      "8000: 0.627875\n",
      "16000: 0.629875\n",
      "32000: 0.6299375\n"
     ]
    }
   ],
   "source": [
    "for n in [10, 50, 100, 1000]:\n",
    "    # Начальное число экспериментов\n",
    "    n_exp = 500\n",
    "\n",
    "    p_0 = 1          #   Вероятность, полученная на предыдущей попытке\n",
    "    delta_ = 0.1     #   \n",
    "    \n",
    "    print(f'n={n}')\n",
    "    while delta_ > 0.001:\n",
    "        count = 0\n",
    "        for k in range(n_exp):\n",
    "            letters = [i for i in range(n)]\n",
    "            a = random.sample(letters, n)\n",
    "            for i in range(n):\n",
    "                if a[i] == i:\n",
    "                    count += 1\n",
    "                    break\n",
    "\n",
    "        p= count/n_exp              # Оцениваем вероятность\n",
    "        print(f'{n_exp}: {p}')\n",
    "        delta_ = abs(p - p_0)        # Считаем изменение вероятности\n",
    "        p_0 = p                      # Новая оценка вероятности заменяет старую\n",
    "        n_exp = round(n_exp * 2)   # Увеличиваем число экспериментов\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "64000\n",
      "0.6299375\n"
     ]
    }
   ],
   "source": [
    "print(n_exp)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  Лабораторная 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Найти вероятность того, что среди этих карт будут представители всех мастей."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000: 0.4317\n",
      "20000: 0.43045\n",
      "40000: 0.42065\n",
      "80000: 0.4275875\n",
      "160000: 0.425125\n",
      "320000: 0.426378125\n",
      "640000: 0.4264109375\n"
     ]
    }
   ],
   "source": [
    "# Число экспериментов\n",
    "n_exp = 10000\n",
    "\n",
    "\n",
    "p_0 = 1          #   Вероятность, полученная на предыдущей попытке\n",
    "delta_ = 0.1     #   \n",
    "\n",
    "#   Колода карт, важна только масть\n",
    "deck = [\"s\"] * 13 + [\"h\"] * 13 + [\"d\"] * 13 + [\"c\"] * 13 \n",
    "\n",
    "while delta_ >= 0.0001:\n",
    "\n",
    "#  Обнуляем счетчик\n",
    "    count_ = 0\n",
    "\n",
    "    for i in range(n_exp):             # Проводим n_exp экспериментов\n",
    "        a = random.sample(deck, 6)     # Выбираем 6 карт без возвращения\n",
    "\n",
    "#   Индийский код\n",
    "        if a.count(\"s\") > 0:\n",
    "            if a.count(\"h\") > 0:\n",
    "                if a.count(\"d\") > 0:\n",
    "                    if a.count(\"c\") > 0:\n",
    "                        count_ += 1\n",
    "\n",
    "    p= count_/n_exp              # Оцениваем вероятность\n",
    "    print(f'{n_exp}: {p}')\n",
    "    delta_ = abs(p - p_0)        # Считаем изменение вероятности\n",
    "    p_0 = p                      # Новая оценка вероятности заменяет старую\n",
    "    n_exp = round(n_exp * 2)   # Увеличиваем число экспериментов\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1280000\n",
      "0.4264109375\n"
     ]
    }
   ],
   "source": [
    "print(n_exp)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Лабораторная 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мешалкин Сборник задач по теории вероятностей n 59.\n",
    "В квадрат с вершинами (0, 0), (0, 1), (1,0), (1,1) наудачу брошена точка М. Пусть (x, y) будут ее координаты. Предполагается, что вероятность попадания в область, лежащую целиком внутри квадрата, зависит лишь от площади этой области и пропорциональна ей.\n",
    "Найти для z = 1/4 P{x*y<z} <br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.705, 0.9, 'H')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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UZMrhw7oY/r//wQMPwKxZUKiQ11GFB0voJiQUKaKbTBYu1GqIoUN1Ae3OO3VXapcu2vb31CmvIzVns2eP/kP84Ye6V+Hll63Blj9ZQjchJyoKHnsMtmzRRbQuXfRYvWuu0RH8o4/q/LsJLhs2aCXLxo3a2K1PH68jCj+W0E3IEoHGjfVs1N279ei8OnW0JLJmTbj0Unj9ddi/3+tIg1+3bt0QEUSEvHnzUq1aNQYMGMDhw4f98vqLFmmN+fHjsGQJtG3rl5c1aVhCN2GhQAG45Rb4+GM9LHjECO3O17u3Vsl06KCj+JMnvY40eLVs2ZLdu3ezfft2hg4dyuuvv86AAQOy/bqTJ2sJasWKWsnSoIEfgjXpsoRuwk65cvDgg7B2LaxaBffdp21X27bVpNK/vz5m/il//vyUK1eOSpUq0alTJzp37sycOXOy/HrOaT+Wbt20znzpUqhc2W/hmnRYQjdhSwQuvlhPt/nlF93AcsUVerhwvXp6e+UVPQnH/FvBggU5mcWPNMePa2OtZ57RRlvz5kHx4n4O0PyLJXQTEfLm1YOv331X59tHjdKmT/3765mpbdvC7NmaiAx89913TJ8+nRYtWmT6e//4QxtsTZ2q1UgTJliDrUCxhG4iTqlSOrf+3XdacTFggE7NdOig8+29esG330bertT58+dTpEgRChQoQOPGjWnSpAmvvfZapl7jxx/1dKFly2DaNK1GsgZbgWMJ3US0mjXhuef08OsFC7S3TFycltfVrKlH6yUmeh1lYDRp0oQ1a9awZcsWjh07xnvvvUfZsmV9/v5vv9X/b7/+qg22OnfOwWBNuiyhG4NubrnmGnjrLd38Mn48lC2rPWWiorQj5LRpussxXBUqVIjo6GgqV65M3rx5M/W977+vG4aKFIHly3UR1ASeJXRj0ihWDO66S+ulf/hB+3L/8INuYCpXTnenfvklJP/rCJfI45wuLN90E9Stq8m8Rg2vo4pcEZ/Qf/31Vx544AFiYmIoUKAAZcuW5bLLLuO1117j0KFDXodnPFatGjz1FCQkaBK/5RZdPG3aFM4/X8vyfvjB6yi9ceqUHlrSvz+0b68NtjIxQxO0Um+ySn1r1KiR16FlKI/XAXhpx44dXH755RQrVowhQ4ZQp04dkpOT2bp1K1OmTKFUqVJ06tTJ6zBNEMiVS7s9NmmiPUjef183zAwZoqV5V1yhZXodOoRmeV5cXFymnn/oENx2m27WGjBADyXJFUbDw5YtWzJ16tR/3JcvBEp1Ijqh33fffeTKlYv4+HgKFy789/21a9emffv2uEgrczA+KVRIF/w6d9YF02nTNLnfcw/07avtfu+4A1q2DM/GU7t3Q5s2sGYNjB6tVUHh5vQmq1ATRv+mZs7+/ftZsGABvXv3/kcyT02s3spkoGJFPWFp40at8rjzTpg/X+uwo6Jg4EB9LFysX689crZsgblzwzOZh7KITejbtm3DOUeNNCs4FStWpEiRIhQpUoSePXue4buN+ScRPRN19Ggdwc6erT1LXnoJLrwQGjbUzUy//+51pFn3+efaYCspSU+Puv56ryPKOadr8lPfBg4c6HVYGYroKZf0fPXVV5w6dYoePXpw7Ngxr8MxISh/fq36uOkm+O03PRd18mSdjunfX6cr7rhDa95DYFoWgIkT4d57tTb/44+hUqWMvyeUNWnShHHjxv3jvhIlSngTTCZEbEKPjo5GRNicpnF21apVAa3JNSa7ypbVY9b69YPvv9fE/tZbuqhaujR06qTJ/eKLg3NHpXMweDA8+6zW4s+erWWd4e50TX6oidgpl1KlSnHNNdcwatQoK080AVGnjk7BJCZqdUizZtrLvUEDfWzECJ2uCRbHj8Ptt2syv/tuHZlHQjIPZRGb0AFef/11kpOTadCgATNmzGDjxo1s3bqVGTNmsHbtWnKHY4mC8VyePDr//M47uit1zBjdYfnQQ7rIet11eliHlzN+v/+uI/Lp02HYMBg3ThucRYrjx4+zZ8+ef9z27t3rdVgZitgpF4Bq1aqxevVqhg8fzuDBg9m5cyd58+alZs2a9OrViz52RpbJYSVLQs+eetuyBaZM0S6FHTtqPfutt+qUTOPGgZuS+eEH/Udlxw6YMUNjiTSff/455cuX/8d9FSpUIDHIG/uIV7XWsbGxLj4+PiDvdesbywF4+97GAXk/Y7IjOVl3XU6erO1+jxyBmBg9JLtLl+wdEtE0rikAi7stTvfx5cu1zXBysp77eeWVWX+vSOBFbhGRlc652PQei+gpF2OCUa5c0KKFjtb37IFJk7Rn++DBegh28+aa7P299PPuu/raxYtrYrdkHnosoRsTxIoW1SPcvvhCe40/84y2+u3WTRuF3XGHHsCcnUZhzumCbIcOWm2zfDlUr+6vKzCBZAndmBBRpYqO0rdtg6+/1pLHOXN0NF+1Kjz+uD6WGUlJetjHQw/BzTfDwoVQpkxORG8CwRK6MSFGRHdsjhunUzIzZkCtWnoYR/XqemLQG2/AgQNnf51Dh6BdO62yefhhmDkTChYMyCWYHOJTQheRViKyRUQSROSRMzynqYisEZENIvKlf8M0xqSnYEGtQvnkE9i5E154Af76S6tmypXTKpl583QkzltvwTffwJdf8kvFS7my9n4WLNBa+HDrlhipMixbFJHcwGjgaiARWCEic51zG1M9pwTwOtDKOfeziIRBV2RjQst55+nUyYABsHKlLpzOmKH17uWKH6Xz4X0cuj6G5FN5aPTLbA6Qlw8f+oLW9zbzOnTjJ77UoV8CJDjntgOIyEygHZC6h1wn4D3n3M8Azrnf/B1odqz+61UOnNxG0zjb5mYiSAOoVTcP+9c2Ys9HDXnpz17wwf2AI3e+fdRrdQXP/7WF5+OC/+CGYLXx978okTcGCI6SaF8+ZFUAdqb6OjHlvtSqAyVFZLGIrBSRrum9kIj0EJF4EYkPhV1XxoS6XHmSKFX/a8pHj6Vg8YS/789f+BcKl9ig+/tN2PBlhJ7e/rS0u5HyAA2AFkBBYLmIfOOc2/qPb3JuHDAOdGNR5sPNmouL9QPg7W7B8a+oMYGydq1Owaz/HKLZRr5m7Uk6UYStS6fQeMpQnqs8FiYt9jrMkHV6Y1Gw8GWEngikbpZZEdiVznPmO+cOO+f2AUuAuv4J0RiTWbt26WEbF18Mq1bByC7xbCjYkDKV36d8zFR68AbP8whz28d5HarxI18S+gogRkSqikg+oCMwN81zPgCuFJE8IlIIuBTY5N9QjTEZOXRID66OidGilgcf1AOu/zsllnxvjtZm7cDIqJdpUPV3uk5sGrGHXIejDKdcnHNJItIHWADkBiY65zaISM+Ux8c65zaJyHzgeyAZGO+cW5+TgRtj/t+pU9oiYPBgrU2/9VbtklitWqonde4MJ98EoMCkxczeAfXr64aiZcusBj0c+NRt0Tk3D5iX5r6xab5+EXjRf6EZY3yxYEHKPPl63VT0/vvQyIfClSpVtLNjmzbQpw9MmJDjoZocZlsJjAlR69bpYdStWmlHxlmztCWAL8n8tOuvh8ce0yPmJk7MuVhNYFhCNybE7N4N99wD9erBd9/Byy/Dxo06dZKVnulPP639YHr3hjVr/B2tCSRL6MaEiMOHtdtiTIzuAr3/fl3wfOCBv9c6syR3bj2ZqFQpPdg6ox4wJnhZQjcmyJ1e8KxeXStYWrfWEfnLL8M55/jnPcqW1RYBp1vzenTujckmS+jGBLHPP9dDpO+8EypV0jnyWbMgJw6kv+wyePFF+OAD/a8JPZbQjQlCGzbouZ5XXw1//qmtbZcv17a5Oen++/Wgi0cfhS+tZ2rIsYRuTBD59Ve4916oU0drw0eMgM2bta48EIdEi8D48foJ4NZbdQHWhA5L6MYEgSNHYOhQTaQTJ0LfvvDDD7rTMzsLnllRrJieL3rwoPZaT0oK7PubrLOEboyHkpO1YqV6dd3lec01uuD56qtadeKV2rX1RKQlS2DQIO/iMJljCd0Yj3zxBcTGalXJeedp8nz3XS1LDAadO8N99+kC6Zw5XkdjfGEJ3ZgA27QJ2raF5s1h/36tAf/mG7jySq8j+7dXXoGGDeGOO7Tm3QQ3S+jGBMhvv0GvXnDRRToaf/55XfC87bbgPc8zf34tk8yTRzcdHTnidUTmbIL0x8iY8HH0KAwfrgue48bpNEZCAjz8MBQo4HV0GatcGaZN094xvXvbpqNgZgndmBySnKyJsEYNXVhs3lzry197DcqU8Tq6zGndGh5/HOLirCtjMLOEbkwO+PJLuOQS6NJFt9V/8YUuLNao4XVkWffkk7rRqU8fPQXJBB9L6Mb40ZYt0K4dNG2qc+ZTp2pHxKZNvY4s+3Ln1lOQypTRzo5//OF1RCYtS+jG+MHevTpyvfBCHY0PG6bJ/fbbg3fBMyvKlNEmXjt3auVLcrLXEZnUwuhHzZjAO3YMXnhBFzzHjtVt+wkJ2gslXI90a9wYXnoJPvxQr90ED0voxmRBcjLMmAEXXAADB0KTJloFMnq0zpmHu759tdfLY4/pJxITHCyhG5NJX32lx7x16qT9yBcu1NFqzZpeRxY4p5t4Va+u/V527fI6IgOW0I3x2bZt0L69jsZ37dIeLPHxWo4YiYoU0VYFhw/raP3kSa8jMpbQjcnA779rn/BateCzz7Qr4tat0LVreC14ZkWtWvDmm3rwxqOPeh2NyeN1AMYEq+PHdRPQ0KHaSvaee+Cpp6BcOa8jCy633QZLl+pCaePG2iLAeCPCxxfG/Jtz8PbbuuD50EN6StD332sViyXz9L30km6k6t5dP70Yb1hCNyaVZct0lNmxox708Nln8PHHWl9uzux0E698+XTTkTXx8oYldGPQ04E6dNDR+M6demrQqlXQsqXXkYWOqCjdSbp+vTYgsyZegWcJ3US0/fuhf38tOfzkE3j6aZ0y6N5dt7qbzLn2WnjiCZgyRRdLTWD5lNBFpJWIbBGRBBF55CzPaygip0TkZv+FaIz/HT+uhzdER8PIkbqNfds2TUaFC3sdXWg7fZRe376wcqXX0USWDBO6iOQGRgOtgVrAbSJS6wzPex5Y4O8gjfEX52D2bC23699fF/LWrNHRZPnyXkcXHk438Tr3XJ1P37/f64gihy8j9EuABOfcdufcCWAm0C6d5/UF3gV+82N8xvjNN9/AFVfoXHnhwjB/vt4uusjryMJP6dK6SPrLL1qvb028AsOXhF4B2Jnq68SU+/4mIhWAG4GxZ3shEekhIvEiEr93797MxmpMlvz4o+5kbNwYtm/XLeurV+t8r8k5l16q01offwzPPed1NJHBl4Qu6dyXdv36VWCgc+7U2V7IOTfOORfrnIstE2pHtpiQ88cfMGCA1pN/9JEe0LBtG9x1ly14BkqvXrrxaPBg7XljcpYvO0UTgUqpvq4IpG3FEwvMFBGA0sB1IpLknJvjjyCNyYwTJ2DMGHjmGU3q3bvrnytUyPh7jX+J6Dmqa9ZoYl+92v4ecpIvI/QVQIyIVBWRfEBHYG7qJzjnqjrnqjjnqgCzgV6WzE2gOQfvv6+bgPr1g/r1NYFMmGBJxEunm3gdOQK33GJNvHJShgndOZcE9EGrVzYB7zjnNohITxHpmdMBGuOL776Dq67Sboj58sG8efDpp1C3rteRGdA6/wkTdCfuww97HU348qk5l3NuHjAvzX3pLoA657plPyxjfLNjBwwapIdNlC0Lb7wBd94JeaztXNC59VZt4vXqq3DZZVptZPzLdoqakHTggJ4UdMEFMGcOPP64Hv3Wo4cl82A2YoQeDnLnnXrmqvEvS+gmpJw8CaNG6Q7PF1/UJlpbt8KQIVC0qNfRmYzky6eHTBcooG12Dx/2OqLwYgndhATn4IMPoHZt3VJet65uK4+Lg4oVvY7OZEalSjB9OmzcCD17WhMvf7KEboJefDw0awY33KD14x99BJ9/Dhdf7HVkJquuvloboU2bpusexj8soZug9fPPcPvt0LChjubGjNGDJq6/XuubTWh77DFo3VqP94uP9zqa8GAJ3QSdv/7SypUaNbR+edAgXfDs2dMWPMNJrlwwdaqeAnXzzXp2q8keS+gmaCQl6Sg8OhqGD9df8i1b4Nln9fQgE35KldLul7t3Q5cu1sQruyyhG885p/PiF12kvT9q1dKP4FOn6ik4Jrw1bKi16Z98AsOGeR1NaLOEbjy1ejW0aAFt2+ro7IMP4IsvoEEDryMzgdSzJ3TurAeMfPaZ19GELkvoxhM7d+opQQ0awLp1Wlu+fj385z+24BmJRLTapVYt6NRJfz5M5llCNwF18KDu6qxeHd5+W/t6JCRA796QN6/X0RkvFS6si+DHjmkTrxMnvI4o9FhCNwGRlKQjsOhoXeRs3x42b9aDD4oX9zo6Eyxq1ICJE/V0qYce8jqa0GMJ3eQo57TzYd26Ok9ao4Z2RnzrLahSxevoTDDq0EFr0//3P/0UZ3xnCd3kmLVr9fT366/XHizvvw9ffqlVDcaczQsv6JGBd9+tn+SMbyyhG7/75RftpnfxxbBqFYwcqQueN9xgC57GN6ebeBUsqE28Dh3yOqLQYAnd+M2hQ3puZ/XqOqXy4IPwww/w3//qL6gxmVGxova537wZ7r3Xmnj5whK6ybZTp2D8eIiJ0bM727bVX8IXX4QSJbyOzoSyFi30Z2r6dN1FbM7OErrJlgULoF49uOceqFYNli+HmTOhalWvIzPh4tFHdR2mXz9dUDdnZgndZMm6dXDttdCqFRw9qv04vv5aT6Mxxp9y5YIpU/Sg7w4drInX2VhCN5mya5dWHtSrBytWwCuvaGvbm26yBU+Tc845B2bNgj17tEXAqVNeRxScLKEbnxw+rAcSxMToaKlfP93h2a+fLXiawIiN1dr0BQtg6FCvowlO1l3anNWpUzB5sm7X371bP/IOHw7nn+91ZCYS9egBS5fq4KJRI532M//PRujmjD77DOrXh7vugsqV9RfpnXcsmRvviMDYsXDhhTr18vPPXkcUXCyhm3/ZsAGuu053eR48qNuvly2Dyy7zOjJjoFAhbeJ14oQ18UrLErr52549uoGjTh0tPxwxAjZt0l8aW/A0waR6dZg0Cb79VjewGWUJ3XDkiC4yxcRop7u+fXXB88EHIX9+r6MzJn033QT9+2sv/ZkzvY4mOFhCj2DJybrgWb06DB6sUywbN+pxYKVKeR2dMRl77jm44gotpd240etovOdTQheRViKyRUQSROSRdB7vLCLfp9yWiUhd/4dq/GnRIj0tqFs33bDx1Vc6LxkT43Vkxvgub15d4ylcWA8Vj/QmXhkmdBHJDYwGWgO1gNtEpFaap/0IXOWcqwMMAcb5O1DjH5s2QZs22iPjjz+0+dHy5TrKMSYUnXeeTrls2aItKCK5iZcvI/RLgATn3Hbn3AlgJtAu9ROcc8ucc3+kfPkNUNG/YZrs+u036NULLrpIt+i/8II20OrYUbdWGxPKmjXTdaCZM2H0aK+j8Y4vv8oVgNRHtiam3HcmdwGfpPeAiPQQkXgRid+7d6/vUZosO3pUNwJFR8Obb8J99+mC50MPQYECXkdnjP8MHKifPvv31yPsIpEvCT29grV0P9SISDM0oQ9M73Hn3DjnXKxzLrZMmTK+R2kyLTkZpk7VI98GDYLmzfWQiddeg9KlvY7OGP873cSrYkXd0RyJY0ZfEnoiUCnV1xWBXWmfJCJ1gPFAO+ec9UPz0OLFesxb165Qtqx+PWeOJndjwlnJktr5c+/eyGzi5UtCXwHEiEhVEckHdATmpn6CiEQB7wFdnHNb/R+m8cXmzdCunc4n7t0L06Zp/+irrvI6MmMCp359/ST62Wd6OEYkybA5l3MuSUT6AAuA3MBE59wGEemZ8vhY4AmgFPC66JbCJOdcbM6FbVLbu1ebFY0dq9uihw/XU9MLFvQ6MmO8cffd2ntoyBA9bLpVK68jCgyfui065+YB89LcNzbVn+8G7vZvaCYjx47pAczDhml723vv1TM9y5b1OjJjvCUCr78Oq1fr1MuqVdpgLtxZwVoISk7WMxZr1IBHHtEplfXrtVzLkrkx6nQTr6QkXSQ9ftzriHKeJfQQ89VX2ge6c2etVlm0CObOhQsu8DoyY4JPdDTExenpWv37ex1NzrOEHiK2boX27aFJEz0GbvJk/SFt1szryIwJbjfeCAMG6BTM9OleR5OzIj6hr169mty5c3P55Zd7HUq69u3TBc4LL9RV+6FDNbl37Wo7PI3x1fDhcOWV2hpgwwavo8k5EZ8S3nzzTXr16sX69evZtGmT1+H87dgx7UceHa3tQe+6S3d4PvaYzg0aY3yXJ4828SpaVNvuHjzodUQ5I6IT+tGjR5k+fTr33HMPN998MxMmTPA6JJzTfhQ1a+r2/Msvh3XrtCTx3HO9js6Y0FW+vP5ubdumZY3h2MQrohP67NmzqVy5MnXq1KFLly5MmTKFkydPehbP0qVaM3vbbVC8uE6xfPwx1Erb29IYkyVNm2qZ7zvv6OajcBPRCX38+PF06dIFgKuuuopChQoxd+7cDL7L/xIStJfzFVfAzp16tNbKldCyZcBDMSbsPfww/Oc/eiLXsmVeR+NfEZvQExISWLp0KZ06dQJAROjcuTPjx48PWAz798MDD+gIfP583aa8daseOpE7d8DCMCaiiGiVWFSUnpf7229eR+Q/Pu0UDUfjx4/n1KlTREVF/X2fS5lU27lzJ5UqVTrTt2bb8eO6CWjIEPjrL13wfOYZKFcux97SGJNKiRK66ahxY+jUCRYsCI9BVESO0JOSkpg8eTLDhw9nzZo1f9/Wrl1LnTp1mDRpUo68r3Mwa5aOyB98UDcIrV0L48ZZMjcm0OrV04HVwoXw1FNeR+MfETlC//jjj9m3bx/33HMPpdKchtyxY0fGjBnD448/Ti4/FnovX65JfPlyPTVowQI9lNkY450779RihKFDdbR+3XVeR5Q9ETlCnzBhAs2aNftXMgfo0KEDP/30E59//rlf3mv7drj1VrjsMvjxRxg/XhsGWTI3waBbt26IyL9ua9as8Tq0gBk1Skfrt98OO3Z4HU32ROQI/WyVLNWqVft7Lj07/vgDnn1WS6Py5NEuiAMGQJEi2X5pY/yqZcuWTJ069R/3lY6gY60KFtRDMRo00CZeX38N+fN7HVXWRGRCz0knTsCYMbrI+ccf0L27Ln6ed57XkRmTvvz581Muwhdxzj9fK19uuAH69dPf4VAUkVMuOcE5XTWvVUt/IBo0gDVrYMIES+bGhIJ27bRGfexYPe0rFFlC94PvvtMuiDffDAUKwCef6KJnnTpeR2ZMxubPn0+RIkX+vrVu3drrkDzz7LN6vkCPHnrGQKixKZds2LEDHn1U+0Oce66WH3bvrnPmxoSKJk2aMG7cuL+/LhjBZxfmyaO/zxdfrE28VqyAYsW8jsp3lnqy4MAB7QcxcqRuRhg8WBtpFS3qdWTGZF6hQoWIjo72OoygUa6cdmZs3lzLGmfN0t2locCmXDLh5EmtWomO1ta2nTrpVv1nnrFkbkw4adJEe6i/+y68+qrX0fjOEroPnIM5c/SQif/+F+rW1eZZkyZBxYpeR2eMOZNff/2V+++/n/PPP5/8+fNToUIFWrduzbx58zL83gEDtOrl4Yd181EosCmXDMTH6w7PJUu0R/lHH+luslD5CGZMpNqxYweXX345RYsWZfjw4dStW5fk5GQWLlxIz549+fnnn8/6/SJ6HmlsrDbxWr06+A9ht4R+Bj/9pKcDvfUWlCmjdal3320Lnia8xMXFeR1CjunVqxfOOeLj4ymSakdfzZo16dy5s0+vUby4bjpq1EjPKfj00+Bu4mVTLmn8+adWrtSoofNngwZpv/KePS2ZGxMq9u/fz/z58+nTp88/kvlpJUuW9Pm16tbVAd2iRfDEE/6M0v8sRaU4eRLefFO36O/bB126aE1qDnbRNcbkkISEBJxz1KxZ0y+v162bzqMPG6ZNvNq08cvL+l3Ej9Cdgw8/1E1AvXtD7dq64DlliiVzY0KVP/oxpfXaa1qf3qWLNtoLRhGd0FetghYt9Dgq52DuXP1YVb++15EZY7IjJiYGEWHTpk1+e80CBXQ+HXRX+LFjfntpv4nIhL5zJ3Ttqv1W1q3T9pnr1kHbtla9Ykw4OOecc7j22msZNWoUhw4d+tfjBw4cyNLrVqumn95XrYL7789mkDnAp4QuIq1EZIuIJIjII+k8LiLyv5THvxeRoBzjHjyolSvVq+up3wMH6oJn796QN6/X0Rlj/On111/HOUdsbCyzZs1iy5YtbN68mTFjxlAnG42W2raFRx7RVh87lpfxY8TZl+GiqIjkBkYDVwOJwAoRmeuc25jqaa2BmJTbpcCYlP8GheRTsH3puUQ/oQfCdu6sC56VK3sdmTEmp1StWpVVq1YxbNgwBg4cyC+//EKpUqWoW7cub7zxRrZee8gQ+PZbWDK9GiUqHfZTxNknGS0eiEhj4Cnn3LUpXz8K4Jwbnuo5bwCLnXMzUr7eAjR1zu0+0+vGxsa6+Pj47F+BDwpV38PRbeUoHf0X9W7ewTlVgucvwJhA+uL33gA0KzXa40hC37G/8jLvmdoUKOTY93PBgB2KISIrnXOx6T3mS9liBWBnqq8T+ffoO73nVAD+kdBFpAfQAyAqKsqHt/aPovV3UKR2Ik2vOWlz5Cailcgb43UIYaNAsZNc2TOBuqXOJX/+4OhQ6UtCTy8Fph3W+/IcnHPjgHGgI3Qf3tsvfp3ZKFBvZUyQa+x1ACYH+bIomgikrsiuCOzKwnOMMcbkIF8S+gogRkSqikg+oCOQ9pTluUDXlGqXRsCfZ5s/N8YY438ZTrk455JEpA+wAMgNTHTObRCRnimPjwXmAdcBCcARoHvOhWyMMSY9PvVycc7NQ5N26vvGpvqzA3r7NzRjjDGZEZE7RY0xJhxZQjfGmDBhCd0YY8KEJXRjjAkTltCNMSZMWEI3xpgwYQndGGPChCV0Y4wJE5bQjTEmTFhCN8aYMGEJ3RhjwoQldGOMCRMZHkGXY28sshf4KYBvWRrYF8D3CzS7vtAWztcXztcGgb++ys65dE+n9iyhB5qIxJ/pHL5wYNcX2sL5+sL52iC4rs+mXIwxJkxYQjfGmDARSQl9nNcB5DC7vtAWztcXztcGQXR9ETOHbowx4S6SRujGGBPWLKEbY0yYCLuELiKtRGSLiCSIyCPpPC4i8r+Ux78XkfpexJlVPlxf55Tr+l5ElolIXS/izIqMri3V8xqKyCkRuTmQ8WWXL9cnIk1FZI2IbBCRLwMdY3b48LNZXEQ+FJG1KdfX3Ys4s0JEJorIbyKy/gyPB0decc6FzQ3IDfwAVAPyAWuBWmmecx3wCSBAI+Bbr+P28/VdBpRM+XPrULk+X64t1fMWAfOAm72O289/dyWAjUBUytdlvY7bz9c3CHg+5c9lgP1APq9j9/H6mgD1gfVneDwo8kq4jdAvARKcc9udcyeAmUC7NM9pB0xx6hughIiUD3SgWZTh9Tnnljnn/kj58hugYoBjzCpf/u4A+gLvAr8FMjg/8OX6OgHvOed+BnDOhdI1+nJ9DigqIgIUQRN6UmDDzBrn3BI03jMJirwSbgm9ArAz1deJKfdl9jnBKrOx34WOGkJBhtcmIhWAG4GxAYzLX3z5u6sOlBSRxSKyUkS6Biy67PPl+kYBNYFdwDrgfudccmDCy3FBkVfyBPoNc5ikc1/aukxfnhOsfI5dRJqhCf2KHI3If3y5tleBgc65UzrICym+XF8eoAHQAigILBeRb5xzW3M6OD/w5fquBdYAzYHzgc9E5Cvn3F85HFsgBEVeCbeEnghUSvV1RXQ0kNnnBCufYheROsB4oLVz7vcAxZZdvlxbLDAzJZmXBq4TkSTn3JyARJg9vv5s7nPOHQYOi8gSoC4QCgndl+vrDjzndNI5QUR+BC4AvgtMiDkqKPJKuE25rABiRKSqiOQDOgJz0zxnLtA1ZVW6EfCnc253oAPNogyvT0SigPeALiEysjstw2tzzlV1zlVxzlUBZgO9QiSZg28/mx8AV4pIHhEpBFwKbApwnFnly/X9jH76QETOBWoA2wMaZc4JirwSViN051ySiPQBFqCr7hOdcxtEpGfK42PR6ojrgATgCDpqCAk+Xt8TQCng9ZSRbJILkk5wZ+PjtYUsX67PObdJROYD3wPJwHjnXLplcsHGx7+/IUCciKxDpygGOudCoq2uiMwAmgKlRSQReBLIC8GVV2zrvzHGhIlwm3IxxpiIZQndGGPChCV0Y4wJE5bQjTEmTFhCN8aYMGEJ3RhjwoQldGOMCRP/B+MZ3QQOwy9vAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#  Пример расположения точки\n",
    "x =  np.array([0.7])\n",
    "y =  np.array([0.6])\n",
    "\n",
    "\n",
    "#  Вершины прямоугольника\n",
    "Rx = [0.0, 0.0, 1.0, 1.0, 0.0]\n",
    "Ry = [0.0, 1.0, 1.0, 0.0, 0.0]\n",
    "plt.axis([-0.1, 1.1, -0.1, 1.1])\n",
    "plt.plot(Rx, Ry)\n",
    "\n",
    "plt.plot(x, y, 'ro')\n",
    "\n",
    "plt.plot([0.0, 1.0], [0.6, 0.6], 'g')\n",
    "plt.plot([0.7, 0.7], [0.0, 1.0], 'g')\n",
    "\n",
    "\n",
    "plt.plot(np.append(x, 1.0), np.append(y, 1.0), 'b')\n",
    "plt.plot(np.append(x, 1.0), np.append(y, 0.0), 'b')\n",
    "plt.plot(np.append(x, 0.0), np.append(y, 1.0), 'b')\n",
    "plt.plot(np.append(x, 0.0), np.append(y, 0.0), 'b')\n",
    "\n",
    "plt.text(x = x+0.01, y = y +0.1, s = \"P\", fontsize=14)\n",
    "\n",
    "plt.text(x = 0.01, y = 0.1, s = \"A\", fontsize=14)\n",
    "plt.text(x = 0.01, y = 0.9, s = \"B\", fontsize=14)\n",
    "plt.text(x = 0.9, y = 0.01, s = \"C\", fontsize=14)\n",
    "plt.text(x = 0.9, y = 0.95, s = \"D\", fontsize=14)\n",
    "\n",
    "plt.text(x = 0.95, y = 0.65, s = \"E\", fontsize=14)\n",
    "plt.text(x = 0.705, y = 0.05, s = \"F\", fontsize=14)\n",
    "plt.text(x = 0.01, y = 0.65, s = \"G\", fontsize=14)\n",
    "plt.text(x = 0.705, y = 0.90, s = \"H\", fontsize=14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#  Нахожу четыре угла в прямоугольнике\n",
    "#  phi_1[DPE, BPG, GPA, EPC]\n",
    "\n",
    "phi_1 = np.arctan(np.array([(1.0 - y[0])/(1.0 - x[0]), \n",
    "                           (1.0 - y[0])/x[0], \n",
    "                           y[0]/x[0], \n",
    "                           y[0]/(1.0 - x[0])]))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000: 0.5915\n",
      "20000: 0.60155\n",
      "40000: 0.601625\n"
     ]
    }
   ],
   "source": [
    "# Число экспериментов\n",
    "n_exp = 10000\n",
    "\n",
    "\n",
    "#  Задаем зерно датчика a \n",
    "#  version=2 требует преобразовать а в целое число, если требуется\n",
    "random.seed(a=12345, version=2)\n",
    "\n",
    "#  промежуточное значение среднего расстояния\n",
    "mean_tmp = 0\n",
    "\n",
    "p_0 = 1          #   Вероятность, полученная на предыдущей попытке\n",
    "delta_ = 0.1     #   \n",
    "\n",
    "\n",
    "while delta_ >= 0.0001:\n",
    "\n",
    "#  Обнуляем счетчик\n",
    "    count_ = 0\n",
    "\n",
    "    for i in range(n_exp):   \n",
    "\n",
    "        x = np.random.uniform(0.0, 1.0, 1)    \n",
    "        y = np.random.uniform(0.0, 1.0, 1)  \n",
    "        if x*y < 0.25 :\n",
    "            count_ += 1\n",
    "    \n",
    "    p= count_/n_exp              # Оцениваем вероятность\n",
    "    print(f'{n_exp}: {p}')\n",
    "    delta_ = abs(p - p_0)        # Считаем изменение вероятности\n",
    "    p_0 = p                      # Новая оценка вероятности заменяет старую\n",
    "    n_exp = round(n_exp * 2)   # Увеличиваем число экспериментов\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "80000\n",
      "0.601625\n"
     ]
    }
   ],
   "source": [
    "print(n_exp)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}