Probability

Consider the following.

What outcomes are possible when rolling:

a)     One six-sided die?
b)     Two four-sided dice?
c)     Three eight-sided dice?
If you roll two dice, what is the smallest sum you can get? What is the largest sum?
If you roll two dice, do you have a greater chance of rolling a total of 4 or 7? Explain.
If you roll two dice 100 times, draw a sketch of what you think the graph would look like if you plotted the sum of the two dice on the horizontal axis and the frequency of the sum on the vertical axis.

When rolling 1 die a large number of times, what would a graph of its distribution look like?
When rolling two dice with 6 faces on each die a large number of times, what would a graph of its distribution look like? How would this graph change if both dice had 8 faces?
When rolling three dice with 4 faces on each die a large number of times, what would a graph of its distribution look like? How would this graph change if all dice had 6 faces or 8 faces?
With a six-sided die, estimate the distribution with a small number of rolls. Roll the die to complete the experiment 10 times and record your resulting score. Calculate your average score over the 10 trials. Now estimate the distribution with a large number of guesses. Roll the die to complete the experiment 10 times and record your resulting score. Calculate your average score over the 10 trials. Compare your results when using a small and large number of rolls.