The Birthday Problem & Other Paradoxes: A Step-by-Step Guide

Описание: [Intro to Conditional Probability] A guide to the birthday problem (aka birthday paradox), the two child paradox (including the child born on Tuesday version) and the rare disease testing paradox explained step by step from first principles (without using Bayes' rule). This video also introduces the concept of conditional probability and probability trees to explain the solution to these 3 counterintuitive probability problems.

The video is intended to be useful as an aid for advanced high school probability classes (e.g. AP statistics) or early undergraduate classes (e.g. intro stats or probability) to help teach topics around Conditional Probability. The main appeal is to show some interesting counterintuitive problems you can solve with these methods. Each of the 3 problems in the topic can be used as a standalone example problem. The license for the video is set to Creative Commons Attribution, so you can use the video for educational purposes as described by the license.

Made for the summer of math exposition 2025 #SoME4

Links:

Python script in collab for the Birthday Paradox: https://colab.research.google.com/dri...

Veritasium video on Bayes' Rule:    • The Bayesian Trap  

3Blue1Brown video on Bayes' Theorem:    • Bayes theorem, the geometry of changing be...  

Wikipedia Link on Two Child Paradox: https://en.wikipedia.org/wiki/Boy_or_...

Wikipedia Link on Birthday Problem: https://en.wikipedia.org/wiki/Birthda...

Wikipedia on Rare Disease Testing Paradox: See similar examples on the Bayes' Theorem page https://en.wikipedia.org/wiki/Bayes%2...

Timestamps:
0:00 Intro to the 3 paradoxes
2:35 The Birthday Problem (aka The Birthday Paradox)
18:45 The rare disease testing paradox
28:10 Two child paradox
32:10 Child born on Tuesday paradox


Thumbnail assets: Icons by Game-icons.net — https://game-icons.net/
Licensed under CC BY 3.0 — https://creativecommons.org/licenses/...

Background Sound:
Ambient Wave 48 (Tribute) by Erokia -- https://freesound.org/s/496757/ -- License: Creative Commons 0