MonteCarlo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import choices, sample\n",
    "from statistics import mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simulates an experiment to generate k independent uniformly random birthdays \n",
    "# and check if there are any repeat birthdays\n",
    "\n",
    "def common_birthday(k):\n",
    "    birthdays = choices(range(1, 366), k=k)\n",
    "    return len(set(birthdays)) != k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4979"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(common_birthday(23) for _ in range(10000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def matching(k=52):\n",
    "    '''Simulates an experiment to permute 'k' cards and check if any jth card's value is j'''\n",
    "    idx_labels = enumerate(sample(range(k), k))\n",
    "    return any(idx == label for idx, label in idx_labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6421"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean(matching() for _ in range(10000))"
   ]
  }
 ],
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