Probability Experiment
Simulate repeated random experiments and watch the estimates converge: a Bernoulli trial (law of large numbers), the Monty Hall problem, the birthday paradox, the coupon collector, and gambler’s ruin. Each run is reproducible from its seed.
Also known as: coin experiment · law of large numbers · monty hall · birthday paradox · gamblers ruin · coupon collector
seeded
Presets
Output
About this tool, tips & examples
What it does
The Probability Experiment tool runs the classic simulations of a statistics course — live, seeded, up to 10,000 trials: Bernoulli trials demonstrating the law of large numbers, the Monty Hall problem, the birthday paradox, gambler’s ruin, and the coupon collector problem. Watch estimates converge to the theoretical answers instead of taking the textbook’s word for it.
The experiments
- Law of large numbers — repeat a success/failure trial and watch the running estimate close in on the true probability you set.
- Monty Hall — switch or stay, simulated; the 2/3 advantage of switching stops being controversial after 10,000 doors.
- Birthday paradox — how often does a group share a birthday? At the default group of 23, just over half the time.
- Gambler’s ruin — a bankroll random walk between zero and a target; see how the odds depend on where you start.
- Coupon collector — how many random draws to collect all N types? (≈ N·ln N, and the simulation shows the painful tail.)
Settings
- Experiment — one of the five above (presets configure each).
- Trials — 1 to 10,000 repetitions; convergence needs volume.
- Experiment parameters — success probability, group size, coupon types, starting and target bankroll, depending on the experiment.
- Seed — the same seed and settings reproduce the identical run, so the whole class can see the same numbers.
Privacy note
Simulations run locally in your browser; nothing is uploaded. Results are Monte Carlo estimates — they wobble around the true values, and that wobble is part of the lesson.
FAQ
Why doesn’t my estimate match the theory exactly? Finite trials never do — that’s variance. Increase the trial count and watch the gap shrink at roughly 1/√n. This is the most important lesson in the tool.
Is the Monty Hall result really 2/3? Yes — run it. Simulation is the argument that finally convinces people the intuitive 50/50 answer is wrong.
Can students verify each other’s results? Seeded runs are identical for everyone — same seed, same settings, same outcome, on any device.