This one could drive you buggy .....

Suppose \(8\) bugs are positioned at the \(8\) corners of a unit cube, (one bug per corner). Each bug, simultaneously, randomly and independently, chooses one of the \(3\) edges adjacent to its corner to travel on, and then does so until it reaches the next corner. (All the bugs travel at the same constant rate.)

The probability that none of the bugs meets any other bug in this process is \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. Find \(a + b\).

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