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add solution to weekend project
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‎day_05/05_monte_carlo_bday_solve.ipynb‎

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{
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"nbformat": 4,
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"nbformat_minor": 0,
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"metadata": {
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"colab": {
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"name": "05_monte_carlo_bday_solve.ipynb",
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"provenance": []
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},
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"kernelspec": {
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"name": "python3",
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"display_name": "Python 3"
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}
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},
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "rsASi4xKIbOe"
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},
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"source": [
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"##Project P5\n",
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"\n",
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"**There is a famous problem in statistics that concerns a room full of people: Same Birthday!**\n",
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"\n",
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"An instructor offers a prize of $20.00 to anyone who thinks that two people in the room have the same birthday.\n",
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"\n",
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"Your assignment is to build a Monte Carlo simulation to tell the instructor how many people need to be in the room to give him/her a better than 50% chance of winning the $20.\n",
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"\n",
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"That is to say how many people need to be in a room in order for the probability of two of them having the same birthday is greater than 50%. Do the same for 95% and 99%."
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "NQRJE-IBADy6"
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},
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"source": [
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"import numpy as np"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "GfQ3DTFRHbrj"
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},
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"source": [
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"### Create functions to run simulations"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"id": "Micplh7EAIRU"
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},
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"source": [
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"def mc_bday(x, y):\n",
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"\n",
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" \"\"\"\n",
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" Calculate probability that at least one pair of x people in a room have the same bday\n",
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"\n",
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" x (int) = number of people in the room\n",
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" y (int) = number of simulations to run\n",
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" \"\"\"\n",
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"\n",
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" # hold results from simulations, create list same length of y\n",
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" results_ls = [0 for x in range(y)]\n",
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"\n",
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" # Conduct y simulations \n",
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" for simulation in range(y):\n",
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"\n",
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" # Create list of bdays of size x and sample with replacement\n",
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" bday_ls = np.random.choice(range(365), size=x, replace=True)\n",
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"\n",
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" # Return 1 if matching bdays found else return 0\n",
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" results_ls[simulation] = [1 if len(bday_ls) != len(set(bday_ls)) else 0][0]\n",
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" \n",
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" # Return the mean of the results_ls\n",
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" return sum(results_ls)/len(results_ls)\n",
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"\n",
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"\n",
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"def find_bdays(probability, num_people, sims):\n",
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" \"\"\"\n",
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" Print how many people are required to have the same birthday for a desired probability\n",
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"\n",
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" probability (list) = desired list of probabilities\n",
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" num_people (int) = range of people to try\n",
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" sims (int) = number of sims to run before determining results of test\n",
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" \"\"\"\n",
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"\n",
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" # use the function to find out how many people it takes to achieve 95% chance of two people having the same birthday\n",
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" for proba in probability:\n",
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" print(f\"**How many people need to be in the room for {proba*100}% chance of having the same birthday**\\n\")\n",
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" for x in range(num_people):\n",
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"\n",
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" #Run x people and sims simulations to determine average\n",
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" results = mc_bday(x, sims)\n",
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" print(f\"Results of {x} people in a room: {results}\")\n",
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"\n",
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" # If results equals probability then stop loop and print results\n",
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" if results >= proba:\n",
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" print(f\"\\n--------------\\nIt takes {x} people to achieve atleast a {proba*100}% chance of 2 people having the same bday.\")\n",
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" print(\"You win $20!\\n--------------\\n\") \n",
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" break\n",
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" else:\n",
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" pass\n",
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" return"
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],
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"execution_count": null,
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"outputs": []
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},
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{
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"cell_type": "markdown",
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"metadata": {
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"id": "Q9tPdUTNGYI4"
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},
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"source": [
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"### Run the experiment"
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]
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},
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{
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"cell_type": "code",
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"metadata": {
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"colab": {
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"base_uri": "https://localhost:8080/"
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},
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"id": "skQgCopJLepG",
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"outputId": "64898769-71a3-4893-d1e7-11b901f712b0"
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},
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"source": [
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"# Probabilities of interest\n",
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"p_ls = [0.50, 0.95, 0.99]\n",
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"\n",
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"# Run experiment\n",
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"find_bdays(p_ls, 100, 5000)"
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],
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"execution_count": null,
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"outputs": [
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{
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"output_type": "stream",
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"text": [
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"**How many people need to be in the room for 50.0% chance of having the same birthday**\n",
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"\n",
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"Results of 0 people in a room: 0.0\n",
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"Results of 1 people in a room: 0.0\n",
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"Results of 2 people in a room: 0.0038\n",
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"Results of 3 people in a room: 0.008\n",
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"Results of 4 people in a room: 0.015\n",
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"Results of 5 people in a room: 0.025\n",
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"Results of 6 people in a room: 0.043\n",
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"Results of 7 people in a room: 0.0552\n",
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"Results of 8 people in a room: 0.0796\n",
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"Results of 9 people in a room: 0.0966\n",
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"Results of 10 people in a room: 0.122\n",
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"Results of 11 people in a room: 0.1384\n",
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"Results of 12 people in a room: 0.1668\n",
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"Results of 13 people in a room: 0.185\n",
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"Results of 14 people in a room: 0.2366\n",
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"Results of 15 people in a room: 0.2516\n",
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"Results of 16 people in a room: 0.276\n",
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"Results of 17 people in a room: 0.3178\n",
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"Results of 18 people in a room: 0.346\n",
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"Results of 19 people in a room: 0.385\n",
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"Results of 20 people in a room: 0.4038\n",
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"Results of 21 people in a room: 0.4526\n",
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"Results of 22 people in a room: 0.4772\n",
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"Results of 23 people in a room: 0.5056\n",
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"\n",
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"--------------\n",
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"It takes 23 people to achieve atleast a 50.0% chance of 2 people having the same bday.\n",
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"You win $20!\n",
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"--------------\n",
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"\n",
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"**How many people need to be in the room for 95.0% chance of having the same birthday**\n",
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"\n",
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"Results of 0 people in a room: 0.0\n",
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"Results of 1 people in a room: 0.0\n",
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"Results of 2 people in a room: 0.0018\n",
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"Results of 3 people in a room: 0.0102\n",
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"Results of 4 people in a room: 0.0144\n",
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"Results of 5 people in a room: 0.028\n",
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"Results of 6 people in a room: 0.0402\n",
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"Results of 7 people in a room: 0.0572\n",
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"Results of 8 people in a room: 0.0756\n",
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"Results of 9 people in a room: 0.0972\n",
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"Results of 10 people in a room: 0.1238\n",
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"Results of 11 people in a room: 0.1428\n",
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"Results of 12 people in a room: 0.1744\n",
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"Results of 13 people in a room: 0.1862\n",
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"Results of 14 people in a room: 0.2246\n",
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"Results of 15 people in a room: 0.2502\n",
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"Results of 16 people in a room: 0.276\n",
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"Results of 17 people in a room: 0.3192\n",
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"Results of 18 people in a room: 0.3548\n",
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"Results of 19 people in a room: 0.3738\n",
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"Results of 20 people in a room: 0.418\n",
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"Results of 21 people in a room: 0.4408\n",
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"Results of 22 people in a room: 0.4718\n",
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"Results of 23 people in a room: 0.4918\n",
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"Results of 24 people in a room: 0.5348\n",
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"Results of 25 people in a room: 0.5614\n",
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"Results of 26 people in a room: 0.6026\n",
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"Results of 27 people in a room: 0.6332\n",
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"Results of 28 people in a room: 0.6562\n",
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"Results of 29 people in a room: 0.6794\n",
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"Results of 30 people in a room: 0.7064\n",
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"Results of 31 people in a room: 0.7282\n",
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"Results of 32 people in a room: 0.7512\n",
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"Results of 33 people in a room: 0.7722\n",
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"Results of 34 people in a room: 0.7886\n",
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"Results of 35 people in a room: 0.8058\n",
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"Results of 36 people in a room: 0.8292\n",
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"Results of 37 people in a room: 0.8502\n",
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"Results of 38 people in a room: 0.8616\n",
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"Results of 39 people in a room: 0.8776\n",
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"Results of 40 people in a room: 0.8904\n",
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"Results of 41 people in a room: 0.9058\n",
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"Results of 42 people in a room: 0.9136\n",
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"Results of 43 people in a room: 0.9294\n",
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"Results of 44 people in a room: 0.9304\n",
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"Results of 45 people in a room: 0.9412\n",
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"Results of 46 people in a room: 0.9542\n",
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"\n",
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"--------------\n",
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"It takes 46 people to achieve atleast a 95.0% chance of 2 people having the same bday.\n",
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"You win $20!\n",
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"--------------\n",
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"\n",
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"**How many people need to be in the room for 99.0% chance of having the same birthday**\n",
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"\n",
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"Results of 0 people in a room: 0.0\n",
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"Results of 1 people in a room: 0.0\n",
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"Results of 2 people in a room: 0.002\n",
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"Results of 3 people in a room: 0.0084\n",
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"Results of 4 people in a room: 0.015\n",
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"Results of 5 people in a room: 0.0246\n",
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"Results of 6 people in a room: 0.0398\n",
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"Results of 7 people in a room: 0.0592\n",
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"Results of 8 people in a room: 0.075\n",
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"Results of 9 people in a room: 0.1002\n",
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"Results of 10 people in a room: 0.1136\n",
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"Results of 11 people in a room: 0.1326\n",
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"Results of 12 people in a room: 0.1714\n",
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"Results of 13 people in a room: 0.1922\n",
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"Results of 14 people in a room: 0.2214\n",
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"Results of 15 people in a room: 0.2506\n",
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"Results of 16 people in a room: 0.2692\n",
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"Results of 17 people in a room: 0.3242\n",
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"Results of 18 people in a room: 0.3366\n",
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"Results of 19 people in a room: 0.3806\n",
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"Results of 20 people in a room: 0.4076\n",
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"Results of 21 people in a room: 0.4432\n",
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"Results of 22 people in a room: 0.479\n",
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"Results of 23 people in a room: 0.5076\n",
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"Results of 24 people in a room: 0.5418\n",
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"Results of 25 people in a room: 0.5604\n",
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"Results of 26 people in a room: 0.5868\n",
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"Results of 27 people in a room: 0.6134\n",
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"Results of 28 people in a room: 0.648\n",
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"Results of 29 people in a room: 0.677\n",
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"Results of 30 people in a room: 0.7074\n",
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"Results of 31 people in a room: 0.7304\n",
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"Results of 32 people in a room: 0.76\n",
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"Results of 33 people in a room: 0.7736\n",
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"Results of 34 people in a room: 0.795\n",
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"Results of 35 people in a room: 0.8156\n",
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"Results of 36 people in a room: 0.8384\n",
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"Results of 37 people in a room: 0.8514\n",
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"Results of 38 people in a room: 0.8702\n",
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"Results of 39 people in a room: 0.8882\n",
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"Results of 40 people in a room: 0.8872\n",
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"Results of 41 people in a room: 0.903\n",
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"Results of 42 people in a room: 0.918\n",
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"Results of 43 people in a room: 0.9244\n",
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"Results of 44 people in a room: 0.937\n",
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"Results of 45 people in a room: 0.9428\n",
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"Results of 46 people in a room: 0.941\n",
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"Results of 47 people in a room: 0.9524\n",
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"Results of 48 people in a room: 0.9604\n",
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"Results of 49 people in a room: 0.9634\n",
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"Results of 50 people in a room: 0.969\n",
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"Results of 51 people in a room: 0.973\n",
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"Results of 52 people in a room: 0.9766\n",
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"Results of 53 people in a room: 0.9798\n",
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"Results of 54 people in a room: 0.9836\n",
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"Results of 55 people in a room: 0.9866\n",
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"Results of 56 people in a room: 0.9882\n",
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"Results of 57 people in a room: 0.992\n",
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"\n",
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"--------------\n",
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"It takes 57 people to achieve atleast a 99.0% chance of 2 people having the same bday.\n",
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"You win $20!\n",
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"--------------\n",
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"\n"
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],
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"name": "stdout"
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}
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]
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}
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]
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}

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