# 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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