logo

... birthday problem.


There's a famous probability exercise called the birthday problem. It's an interesting problem for sure, but typically it is calculating the wrong thing. In this series of videos we'll explore what this means.


Notes

The code that does all the simulation and plotting is listed below.

import numpy as np
import matplotlib.pylab as plt

def calculate(room = 20):
    return 1 - np.prod((365 - np.arange(room))/365)

def simulate(room = 20, n_sim = 1000):
    hit = 0 
    for i in range(n_sim):
        n_bday = np.unique(np.random.randint(1, 365, room)).shape[0]
        hit += n_bday == room
    return 1 - hit/n_sim

plt.plot([calculate(r) for r in range(1, 35)], label="calculated")
plt.plot([simulate(r) for r in range(1, 35)], label="simulated")
plt.legend();

Feedback? See an issue? Something unclear? Feel free to mention it here.

If you want to be kept up to date, consider getting the newsletter.