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.
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 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();
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