Simulating the probability of rolling a 6

The applet below allows for investigating the probability of rolling a 6 on a fair die via simulation. The plot in the top left corner shows the probability associated with each outcome of a die roll. When the Roll button is clicked, n simulations of the experiment of rolling a die are performed. The results of the simulations are shown in the plot below the top plot. If the Animate option is checked, the display will show each outcome dropping into the second plot. To stop an animation uncheck the Animate option. The individual outcomes are shown in the text field to the far right of the applet. The center plot shows the cumulative proportion of times that an event of rolling a 6 occurs in red. The green line in the plot reflects the true probability of rolling a 6. As the experiment is conducted more and more times, the cumulative proportion should converge to the true value. Things to try with the applet:

  • Run the simulation 10 times (n = 10). How close is the cumulative proportion to the true value? Click the Reset button to the clear the results, and then run the simulation 10 times again. How does the cumulative proportion compare to your previous value? Repeat this process a few more times and continue to compare values of the cumulative proportion.
  • Run the simulation 1000 times (n = 1000). How close is the cumulative proportion to the true value? Click the Reset button to the clear the results, and then run the simulation 1000 times again. How does the cumulative proportion compare to your previous value? Repeat this process a few more times and continue to compare values of the cumulative proportion.