MODERN ALCHEMIST

Statistical Probability

An experiment was carried out below to see if it would yield results appropriate for a probability/statistics laboratory. Six dice were thrown 100 times, and the total was recorded. The math to calculate the average is shown below, followed by a bar graph indicating how many times each score was reached.

 (0.02)12
 (0.01)13
 (0.04)14
 (0.05)15
 (0.06)16
 (0.05)17
 (0.09)18
 (0.08)19
 (0.13)20
 (0.13)21
 (0.07)22
 (0.06)23
 (0.07)24
 (0.02)25
 (0.04)26
 (0.02)27
 (0.04)28
 (0.01)29
 (0.00)30
 (0.00)31
+(0.01)32
---------
    20.37

After 100 dice rolls, we can see that some pattern appears to the graph, resembling a hill, or a bell. You may have heard the expression bell curve.

Can we match this curve to a probability function?

As a test, the experiment was changed to just three dice. With three dice, there are 216 possible combinations. The score for each possible combination was calculated, then the number of times each score occurred was computed.

In the illustration below, the grey maps out the above distribution. Three dice were rolled, and after each 20 scores, a new frame was prepared for the animation.

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