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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?

 Mar 5, 2021
 #1
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of rolling a sum of  ??

 Mar 5, 2021
 #2
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On both dice, only the faces with the numbers $3,6$ are divisible by $3$. Let $P(a) = \frac{2}{8} = \frac{1}{4}$ be the probability that Juan rolls a $3$ or a $6$, and $P(b) = \frac{2}{6} = \frac 13$ that Amal does. By the Principle of Inclusion-Exclusion,

 Mar 5, 2021

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