Statistics and Dice

The Flash simulation below rolls dice and displays histograms of the results. By playing around with it, you can get a sense of how probability and reality often differ. Probability predicts that you will get equal amounts of each result in the long run. But how long is the long run? Do you ever get equal amounts of each result? Are the results repeatable? predictable?

After completing these investigations, you may want to play with some other simulations involving dice.

Investigations

1. Using five dice, how many rolls does it take to get two sixes in the same roll? Try this several times.
2. Using five dice, how many rolls does it take to get three sixes in the same roll? Try this several times.
3. How long do you think it would take to get four sixes in the same roll if only five dice are rolled?
4. Roll five dice one hundred times. What number appeared most often? least often? By how much were the most and least separated? Try this several times.
5. Roll ten dice one hundred times. What number appeared most often? least often? By how much were the most and least separated? Try this several times.
6. Do the dice seem to be fair?

Another set of dice

Repeat the above investigations with the Flash simulation below. Do you notice any differences?