With what probability, starting at node $g$, does node $d$ get hit before node $e$ in the graph below?
What is the expected value of number of steps you need to hit $\{d,e\}$ (at least one of them) starting from node $g$?
Please help me answering the questions, I have no idea where to start.
The random walk on the graph is assumed to be uniform.
Best Answer
Let $u(x)$ be the probability, starting at node $x$, that you hit $d$ before $e$. Thus $u(d) = 1$ and $u(e) = 0$. For other nodes $x$, $u(x)$ is the average of $u(y)$ over the neighbours $y$ of $x$. Solve the system of equations...