Probability

Probability laboratory

Choose an experiment and increase the number of trials: compare what happens with what mathematics predicts.

Distribution lab

Simulation results and theoretical probabilities
Outcome Count Observed frequency Theoretical probability Difference Histogram

Blue: observed frequency. Orange: theoretical probability. Bars are scaled to the experiment’s largest theoretical value; the percentages in the table are the actual values.

Trials run in your browser; results are not saved on the server.

What does the simulation show?

Observed frequency is the number of times an outcome occurs divided by the number of trials. Theoretical probability is calculated from the possible outcomes in the stated model. Difference is shown in percentage points.

With many trials, frequencies tend to approach theoretical probabilities, but they need not match exactly: chance still creates fluctuations after thousands of trials.