This simple activity introduces the student to random events, addition, graphing, combinations, probability distributions, and the law of large numbers.

## Activity

Collect two six-sided dice and a pencil. Click to expand the “Roll the Dice” worksheet shown at the right and print out a copy. (Alternatively use graph paper or draw a similar worksheet.) Sit at a table or flat worksurface, and carry out the following steps:

1. Roll both dice.
2. Add the resulting dot counts together to obtain a number ranging from 2 and 12.
3. Mark an X in the grid box above that number on the worksheet.
4. Repeat this a few dozen times. As numbers repeat, stack the X marks to create a bar chart.

What pattern emerges?

How can that pattern be explained?

## Analysis

Although the result of each individual die is uniformly distributed, the sum of the two dice is not. This is because there is only one outcome that results in a sum of 2 or 12, yet there are 6 outcomes that result in a 7. The table below enumerates the possible outcomes.

The student is likely to notice that the resulting pattern does not conform to the predicted probabilities. The nature of a random event is that it is not predictable and variation in the outcome is expected. As the number of trials increases, the resulting pattern is likely to conform more closely to the predicted probabilities.

Sum of Two Dice
+ 1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12