{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# What is the probability of having the same PID twice in a day?\n",
    "\n",
    "The birthday problem\n",
    "https://www.probabilisticworld.com/birthday-problem-python-simulation/\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import randint\n",
    " \n",
    " \n",
    "NUM_PEOPLE = 23\n",
    "NUM_POSSIBLE_BIRTHDAYS = 365\n",
    "NUM_TRIALS = 10000\n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    " \n",
    "def generate_random_birthday():\n",
    "    birthday = randint(1, NUM_POSSIBLE_BIRTHDAYS)\n",
    "    return birthday\n",
    " \n",
    " \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generate_k_birthdays(k):\n",
    "    birthdays = [generate_random_birthday() for _ in range(k)]\n",
    "    return birthdays\n",
    " \n",
    " \n",
    "def aloc(birthdays):\n",
    "    unique_birthdays = set(birthdays)\n",
    " \n",
    "    num_birthdays = len(birthdays)\n",
    "    num_unique_birthdays = len(unique_birthdays)\n",
    "    has_coincidence = (num_birthdays != num_unique_birthdays)\n",
    " \n",
    "    return has_coincidence\n",
    " \n",
    " \n",
    "def estimate_p_aloc():\n",
    "    num_aloc = 0\n",
    "    for _ in range(NUM_TRIALS):\n",
    "        birthdays = generate_k_birthdays(NUM_PEOPLE)\n",
    "        has_coincidence = aloc(birthdays)\n",
    "        if has_coincidence:\n",
    "            num_aloc += 1\n",
    " \n",
    "    p_aloc = num_aloc / NUM_TRIALS\n",
    "    return p_aloc\n",
    " \n",
    " \n",
    "p_aloc = estimate_p_aloc()\n",
    "print(f\"Estimated P(ALOC) after {NUM_TRIALS} trials: {p_aloc}\")\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the linux PID pool in 32,768 and I have restarted my process 200 times today.\n",
    "\n",
    "$$\n",
    "P(ALOC) + P(NC) = 1\n",
    "$$\n",
    "\n",
    "$$\n",
    "P(ALOC|k) = 1 - ( 32,768! / (32,768**200 * (365 - 200 )) ) = 0.46\n",
    "$$\n",
    "\n",
    "[ALOC] = at least one coincidence\n",
    "[NC] = No Coincidence\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM_PEOPLE = 200\n",
    "NUM_POSSIBLE_BIRTHDAYS = 32768\n",
    "NUM_TRIALS = 10000\n",
    "p_aloc = estimate_p_aloc()\n",
    "print(f\"Estimated P(ALOC) after {NUM_TRIALS} trials: {p_aloc}\")"
   ]
  }
 ],
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  "language_info": {
   "name": "python"
  },
  "orig_nbformat": 4
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