File:Birthday paradox approximation.svg
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Original file (SVG file, nominally 768 × 480 pixels, file size: 27 KB)
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Summary
| Description |
English: A graph comparing the accuracy of an approximation of the probability that in a room with n people (shown along the horizontal axis), some two (or more) will share a birthday. The black line, represents the computed probability. The red line represents the approximation
Español: Comparación entre la probabilidad de que dos personas (o más) en un cuarto compartan su cumpleaños (línea negra) y la aproximación: |
| Date | |
| Source | Own work |
| Author | Nicoguaro |
| SVG development |  This W3C-invalid plot was created with Matplotlib. |
| Source code | Python code#from __future__ import division # Python 2
import numpy as np
from scipy.special import perm
import matplotlib.pyplot as plt
from matplotlib import rcParams
rcParams['font.family'] = 'serif'
rcParams['font.size'] = 14
rcParams['svg.fonttype'] = 'none'
num = np.linspace(1, 100, 100)
p = 1 - perm(365, num)/365.**num
p_approx = 1 - np.exp(-num**2/730)
plt.figure(figsize=(8, 5))
plt.step(num, p, "k", lw=2)
plt.plot(num, p_approx, "r", lw=1)
plt.xlabel(r"Number of people - $n$")
plt.ylabel("Probability of a pair")
plt.xlim(0, 100)
plt.ylim(0, 1)
plt.grid(True)
plt.legend([r"Probability: $1-\frac{365!}{365^n (365 - n)!}$",
r"Approximation: $1-e^\frac{-n^2}{2\cdot 365}$"], loc=4)
plt.savefig("Birthday paradox approximation.svg")
plt.show()
|
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 4.0 International license.
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- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 04:49, 20 October 2025 | | 768 × 480 (27 KB) | wikimediacommons>Based5290 | use text for text instead of paths |
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