Birthday Problem


Massachusetts Institute of Technology


June 13, 2020

We have all been there, classic math riddle:

How many people need to be in one room so that the probability of two of them having the same birthday is more than 0.5?

In a recent bootcamp exercise we tackled this in python and I wanted to share, just because it’s fun. I did it for a range of probabilities. My solution is probably not the fastest/shortest/most pythonic, but it’s a little thing I put out there so, if you want to use/improve it, please do!

import numpy as np
import matplotlib.pyplot as plt

def prob(n):
    numerator = np.math.factorial(365) / np.math.factorial(365-n)
    denominator = 365 ** n
    return(1 - numerator/denominator)

probs = list(map(prob, range(100)))

plt.plot(range(len(probs)), probs)

A bad translation into R, it would be something like:

prob <- function(n){
  numerator = exp(lfactorial(365) - lfactorial(365-n))
    denominator = 365 ** n
    return(1 - numerator/denominator)

probs = sapply(0:99, function(n) prob(n))

plot(0:99, probs, type="l",
     main="Probability of 2 people having same birthday",
     xlab = "People in a room", ylab="probability")



BibTeX citation:
  author = {Andina, Matias},
  title = {Birthday {Problem}},
  date = {2020-06-13},
  url = {},
  langid = {en}
For attribution, please cite this work as:
Andina, Matias. 2020. “Birthday Problem.” June 13, 2020.

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