Probability Simulation

Dice are often used to teach about the ideas of probability and random events. This app has two options that allow users to explore the space of dice-based probabilities. In the probability distribution simulation, one can toss all dice, one at a time or all at a time or continuously, for an experimental probability distribution. With the theoretical probability option, one can specify the number of dice and the sum of interest and enumerate all the different cases for the chosen sum, which leads to a theoretical probability. There are some interesting questions to explore. For example, if one tosses three dice, what is the probability that the sum of them is 12? In simple cases and special sums, one can use a bit of combinatorics. In cases of many dice and an arbitrary sum, a simulation may be more appropriate to get started.