---
slug: the-birthday-paradox
title: "The Birthday Paradox"
date: "2021-11-11T06:46:00-04:00"
---
> How many people have to be in a room before the probability that there
> is a shared birthday is greater than 50%?

This is called the [Birthday Problem][bp], and the solution is known as
the *birthday paradox*.  It is interesting because the answer is
counterintuitive and the ramifications affect the security of
[cryptographic hash algorithms][hash].

The explanation is a bit long for a blog post, so I wrote a full
article:

[The Birthday Paradox][bp]

[bp]: {{< relref "/content/articles/the-birthday-paradox.md" >}}
  "The birthday Paradox"
[combinatorics]: https://en.wikipedia.org/wiki/Combinatorics
  "The mathematics of counting."
[set theory]: https://en.wikipedia.org/wiki/Set_theory
  "The mathematics of sets."
[probability]: https://en.wikipedia.org/wiki/Probability
  "The mathematics of determining how likely an event is to occur."
[hash]: https://en.wikipedia.org/wiki/Cryptographic_hash_function
  "Cryptographic hash algorithm."
[intersection]: https://en.wikipedia.org/wiki/Intersection_(set_theory)
  "Intersection."
[independent]: https://en.wikipedia.org/wiki/Probability#Independent_events
  "Independent events in probability theory."
[discrete]: https://en.wikipedia.org/wiki/Random_variable#Discrete_random_variable
  "A random value with a countable number of possible values."
[joint probability]: https://en.wikipedia.org/wiki/Joint_probability_distribution#Coin_flips
  "Joint probability."
[die]: https://en.wikipedia.org/wiki/Dice
  "Dice."
[factorial]: https://en.wikipedia.org/wiki/Factorial
  "Factorial unary operator."
[ruby]: https://ruby-lang.org/
  "Ruby programming language."
[csv]: https://en.wikipedia.org/wiki/Comma-separated_values
  "Comma-separated values."
[html]: https://en.wikipedia.org/wiki/HTML
  "HyperText Markup Language"
[yaml]: https://en.wikipedia.org/wiki/YAML
  "YAML Ain't a Markup Language"
[hugo-table-shortcode]: https://github.com/pablotron/hugo-shortcode-table
  "Table shortcode for Hugo."