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---
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."
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