About

probability.app is an interactive field guide to probability. Start with a question, make a prediction, and use a model to explore the answer. The collection brings together distributions, laws, paradoxes, and puzzles, with foundations and learning paths to connect them.

How to use it

Each experiment combines an explicit model with controls you can change. A theoretical probability and a simulated frequency answer different questions: one is calculated from the model, while the other varies with the random sample. Numerical outputs and worked examples help connect the picture to the calculation.

The Copy experiment link control preserves supported parameters and random seeds in the URL. Share that link to revisit the same setup. Reset starts again with the page defaults. Simulated observations stay in your browser.

Editorial approach

We aim to state assumptions, distinguish exact results from approximations, and include boundary cases where familiar rules fail. Expanded lessons include prediction checks, worked calculations, and further reading. Pages are being reviewed in stages; an updated date marks a substantive revision, not a guarantee that every possible question is covered.

Numerical regression checks and a rendered-page validator run locally alongside type checks. Corrections to formulas and explanations take priority over adding topics. The site is an educational resource: real applications also require checking whether the model describes the data-generating process.

Technology and privacy

Pages are built with Astro and MDX. Interactive experiments use Svelte and D3 scales. Cloudflare hosts the site. The site records page views and referrers for aggregate usage analysis; experiment controls do not submit simulated observations. The optional subscription form uses Cloudflare Turnstile for spam protection and stores the email address needed to send updates.

Stay in touch

The form below subscribes you to new lessons and site updates. Subscription is optional, requires email confirmation, and includes an unsubscribe link. You can also follow the RSS feed.