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jmc

counting and probability junior

Problem

The faces of an octahedral die are labeled with digits through . What is the probability, expressed as a common fraction, of rolling a sum of with a pair of such octahedral dice?
Solution
There are 8 digits upon which the die can land in the first roll and 8 digits upon which the die can land in the second roll. Thus, there are pairs of digits that can result from two rolls. Of these, only two will produce a sum of 15: 8 and 7 or 7 and 8. Thus, the probability of rolling a 15 is .
Final answer
\frac{1}{32}