There are many activities involving probability and rolling dice. One activity by MathWire is called "The Game of Pig" and teaches students the difference between ideal probability and actual events. Students roll a die and receive that many points, keeping individual totals. If anyone throws a one, though, the whole class loses any points gained during that round. The likelihood of rolling a 1 is 1/6, but it will seem to happen more often when applied to a group.
Mathematics is one of the available categories in most school science fairs. Probability science projects can analyze probability functions in areas such as hitting streaks in baseball, using historical data to predict likelihood of earthquakes, or the likelihood of hurricanes hitting a particular location.
There are several game show simulations online that can help students understand the concepts of probability. The game Plinko, from "The Price is Right," involves sliding discs down a board with round pegs that bounce the discs from side to side. There are different channels at the bottom of the board representing different amounts of money. Simulations like the one on the University of Colorado website allow students to build a histogram showing the probability of different outcomes in Plinko.
Split students into groups and have them design a spinner with various outcomes. Have students ascertain what the probability of each spot on the spinner is. For advanced classes, allow them to size their spaces differently, as long as there is a common factor. For example, students could have spaces sized 1/3, 1/4, and 1/12 of the wheel, because 12 is a common multiple for 3 and 4.