# Probabilities of a multi facets dice

An octahedron is a three dimensional shape with eight sides that are equilateral triangles. This shape is used as a die in games such as Dungeons and Dragons because all eight sides come up with equal probability.

A. Assuming the sides are numbered 1 through 8, and a person throws two octahedral dice, what are the possible sums? ( Explain your answer)

B. Which sum has the highest probability? What is this probability? (Explain your answer).

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#### Solution Preview

The minimum value of each die is 1, therefore the minimum value of the sum of two dice rolled together is 1+1=2.

The maximum value of each die is 8, therefore the maximum value of the sum of two dice rolled together is 8+8=16.

Thus:

The possible sums can be any integer between the numbers 2 and 16 (inclusive).

The most common sum will be 9, since it can utilize all the possible numbers.

For example ...

#### Solution Summary

The solution determines the probabilities of a multi facets dice.