# This program simulates the following process: several people
# announce their birthdays until two of them share a birthday.
# We assume that no one is born of Feburary 29th (sorry!),
# and that every day is equally likely to be someone's birthday.
# The function birthday() counts the number of people before
# we get a match. The function makehist(n) runs n trials of
# this process and then draws a histogram of the data.
# Are you surprised by how small the values are?

import random
import numpy as np
import matplotlib.pyplot as plt

def birthday():
    birthdays = []
    while True:
        newday = random.randint(0,364)
        if newday not in birthdays:
            birthdays.append(newday)
        else:
            return len(birthdays) + 1

def makehist(n):
    bds = [birthday() for _ in range(n)]
    hist, bins = np.histogram(bds, bins=20)
    widths = np.diff(bins)
    plt.bar(bins[:-1], hist, widths)
    plt.show()

makehist(100)