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 $a+b$ .

Try more questions on Platonic Solids

Image credit: http://loki3.com/