# Transcendental Dice Rolls

Probability Level 5

Three fair 6-sided dice each have their sides labeled $0,1,e,\pi, i, \sqrt{2}$. If these dice are rolled, the probability that the product of all the numbers on the top face is real can be expressed as $\frac {a}{b}$, where $a$ and $b$ are coprime positive integers. What is the value of $a+b$?

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