Birthday Paradox

An interactive app that visualizes the Birthday Paradox through graph theory and probability analysis.

Overview

The Birthday Paradox shows that in a group of just 23 people, there's over a 50% chance two people share a birthday - a result that is very counterintuitive. This project models that problem as a graph and visualizes how the probability shifts as group size grows.

Technical Highlights

• NetworkX (Graph Theory): Constructs a graph where people are nodes and shared birthdays are edges, making the abstract probability problem concrete and traversable.
• Plotly: Renders interactive network graphs and probability curves, allowing real-time exploration of the data.
• Streamlit: Powers the frontend as a single-page data application.
• Docker and Docker Compose: Fully containerized for a consistent, one-command deployment.

Features

• Interactive Graph: Watch nodes and edges form in real-time as shared birthdays are detected in the group.
• Probability Curve: See how the likelihood of a shared birthday climbs as group size increases.
• Live Statistics: Side-by-side comparison of theoretical probability vs. actual matches in the simulation.
• Adjustable Group Size: Explore any group from 2 to 366 people using an interactive slider.

Project Structure

birthday-paradox/
├── app.py                  # Streamlit entry point
├── docker-compose.yml      # Service orchestration
├── Dockerfile              # Container definition
├── requirements.txt        # Dependencies
└── processors/
    ├── __init__.py
    └── processors.py       # Birthday generation and graph logic

Getting Started

Prerequisites

• Docker and Docker Compose (recommended)
• Python 3.11+ (if running locally)

Docker (Recommended)

1. Clone the repository:

   git clone https://github.com/your-username/birthday-paradox.git
   cd birthday-paradox

2. Build and start the app:

   docker compose up --build

3. Visit http://localhost:8501 in your browser.

License

This project is licensed under the MIT License.