Simulate coins, dice, cards, and the birthday paradox — the exact theoretical probability derived step by step, then verified with an animated Monte-Carlo run.
Tip: use samples, upload, copy, download, and send-to actions inside the workspace where available.
Probability Lab is a free, browser-based tool that helps you get the job done quickly. Simulate coins, dice, cards, and the birthday paradox — the exact theoretical probability derived step by step, then verified with an animated Monte-Carlo run. It's built for speed and privacy: Everything runs locally in your browser — your data is never uploaded to a server. No sign-up, no installs, and no daily limits.
Use this tool as the focused step in a larger browser-based workflow.
Review the preview, copy or download the result, and keep everything local in your browser.
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Open tool1 trial = flip 3 coins with P(heads) = 0.5 and count heads.
Each coin lands heads with probability p = 0.5 and tails with probability 1 − p = 0.5. One trial flips 3 coins and counts the heads.
The number of heads X in n = 3 independent flips follows the Binomial(n, p) distribution:
“At least 2” means k = 2, 3, …, 3. Add the binomial term for every qualifying k:
Seeded runs are fully reproducible — the same seed always produces the same trials, and Step ◀ rewinds the PRNG itself.
Press Play for an animated run, or Step ▶ to advance one batch at a time.
Running estimate p̂ = hits ÷ trials (solid) settles onto the theoretical value (dashed) as trials grow.
Empirical outcome frequencies next to the exact distribution. Full-strength bars are the event outcomes.
