interview question A bug crawls along the edges of a regular tetrahedron

interview question A bug crawls along the edges of a regular tetrahedron

A bug crawls along the edges of a regular that after it has crawled a tetrahedron ABCD with edges length 1. It starts at A and at each vertex chooses its next edge at random (so it has a 1/3 chance of going back along the edge it came on, and a 1/3 chance of going along each of the other two). Find the probability that after it has crawled a distance 7 it is again at A.

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Probability and discrete mathematics:

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