Demonstration of Long-Run Empirical Probability
This demonstration illustrates how precise measurements of probability arise from the patterns created by large numbers of individually random events.


  1. Click on the coin to flip it. Select one of the "auto" choices from the list on the top right to make the coin flip repeatedly at different speeds.
  2. As the number of times the coin is flipped increases, the graph shows the percentage of heads out of all flips. Initially it may be some distance of from the midpoint at 1/2, but as the number of flips gets larger and larger, the tendency is always for the graph to approach the line. When the graph runs off the right-hand side of the screen, the graph will recale itself automatically to show a larger range.
  3. Click the "bias" to make the coin biased in favor of either heads or tails.
  4. Click the reset button in the top left corner to set the count back to zero.