# Random "Tetrahedron" Walk

**Discrete Mathematics**Level 3

Call the vertices of a tetrahedron, A, B, C, and D.

A bug starts on vertex A. Every second he randomly walks along one edge to another vertex. What is the expected value of the number of seconds it will take for him to reach the vertex, D?

**Clarification:** Every second he chooses randomly between the three edges available to him, including the one he might have just walked along.

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