0
$\begingroup$

A little change in that problem:

Logic question: Ant walking a cube

There is a cube and an ant is performing a random walk on the edges where it can select any of the 3 adjoining vertices with equal probability. What is the expected number of steps it needs till it reaches the diagonally opposite vertex?

Taking the cube image there, and starting in 1 and ending in 8,

What would be the expected number of steps without passing by vertex 5?

Thanks!

  • 1
    If by "without passing by vertex 5" you mean that the random walk is performed on the cube without vertex 5 (or, equivalently, you want the conditional expectation value given the condition that the walk doesn't pass by vertex 5), then you can use the same kind of analysis that Sivaram applied in the other question (except for the symmetry) to get the result for this one.2011-03-25
  • 0
    Please clarify what you mean by "without passing by vertex 5" since it appears there are different interpretations and you probably mean only one of them.2011-03-25

1 Answers 1