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File:Birthday paradox approximation.svg

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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 1−e−n22⋅365
    Español: Comparación entre la probabilidad de que dos personas (o más) en un cuarto compartan su cumpleaños (línea negra) y la aproximación: 1−e−n22⋅365
    Date
    Source Own work
    Author Nicoguaro
    SVG development
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     The source code of this SVG is invalid due to an error.
     This W3C-invalid plot was created with Matplotlib.
     The file size of this SVG plot may be irrationally large because its text has been converted to paths inhibiting translations.
    Source code
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    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:
    w:en:Creative Commons
    attribution
    This file is licensed under the Creative Commons Attribution 4.0 International license.
    You are free:
    • to share – to copy, distribute and transmit the work
    • to remix – to adapt the work
    Under the following conditions:
    • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.

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    inception

    11 February 2016

    media type

    image/svg+xml

    height

    450 pixel

    width

    720 pixel

    data size

    27,639 byte

    checksum

    6911fd8c49107e27838df9ea692b74e5318a4617

    determination method or standard: SHA-1

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    Date/TimeThumbnailDimensionsUserComment
    current03:49, 20 October 2025Thumbnail for version as of 03:49, 20 October 2025768 × 480 (27 KB)Based5290use text for text instead of paths
    05:12, 28 September 2025Thumbnail for version as of 05:12, 28 September 2025768 × 480 (43 KB)Based5290tighter bounds
    05:08, 28 September 2025Thumbnail for version as of 05:08, 28 September 2025768 × 480 (44 KB)Based5290Corect error in legend
    16:09, 11 February 2016Thumbnail for version as of 16:09, 11 February 2016720 × 450 (54 KB)NicoguaroUser created page with UploadWizard

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