Probability Experiment Lab
Specify a finite experiment, then compare its exact outcome counts with a reproducible local simulation. See where observed frequencies differ from expected counts and how one selected outcome develops across trials. The seed reproduces a teaching sample; it does not predict physical tosses.
Key features
- Integer convolution gives exact favorable and total sequence counts for fair independent coins and dice
- A documented 32-bit seeded pseudorandom generator makes every repeated run reproducible
- Expected and observed counts, differences and a selected event's at-least-once chance
- A labeled five-percent rare-event rule and approximate Wilson 95% interval for the observed rate
- Chunked trials with pause, resume and cancel; partial results are retained
- Versioned JSON plus distribution and convergence CSV exports
How to use
- Choose one to twelve fair coin flips or one to four fair dice and select a supported face count.
- Select the number of heads or the dice sum to follow; enter up to 100,000 trials and a 32-bit seed.
- Run the experiment, pausing or cancelling if needed; compare the exact distribution, expected counts and sampled results.
- Inspect the selected outcome's convergence graph and checkpoint table, then export JSON or CSV.
Use cases
- Show why 2d6 sums are not equally likely even though each die face is fair
- Reproduce a classroom coin-flip simulation from the same rule and seed
- Explain why a rare event may not appear in a finite sample
Frequently asked questions
Is the theoretical probability simulated?
No. The exact numerator counts all equally likely sequences under the explicit assumption of independent fair faces. Only the observed counts come from seeded pseudorandom trials.
What does rare mean here?
This page labels a selected event rare when its exact per-trial probability is at most 5%. That threshold is a teaching convention, not a statistical test.
Can the same seed predict real dice?
No. It repeats this tool's deterministic pseudorandom sequence for the same rule and run length. Physical coins, dice and biased devices can behave differently.
What does the 95% interval mean?
The Wilson score interval is an approximate uncertainty summary for the observed event proportion under independent Bernoulli trials. It is not a guarantee or evidence that the fair-face model is true.
What happens when I cancel?
The next bounded chunk is not scheduled. Completed trials, their distribution and checkpoints remain visible and exportable with a cancelled status.
Privacy
All rules, seeds and sampled results are calculated in this browser tab. They are not submitted to an API or saved after leaving. Downloads occur only when you choose them.
Comments & questions