Wandering on a tetrahedron
The vertices of a tetrahedron are labeled \(A, B, C\) and \(D\). A bug starts out on \(A\) and moves randomly along an edge to another vertex every 10 seconds. After 20 seconds, what is the probability that the bug will end up at \(B\)?
If the probability can be written as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).
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