At point $A$, the probability of moving up is $q$ and the probability of moving down is $p$. At point $B$, the probability of moving left is $x$, the probability of moving right is $y$ and the probability of moving up is $z$. Every point on the vertical line except the bottom one is similar to point $A$ and every point on the bottom horizontal line is similar to point $B$. What's the probability of an article ever reaches point $C$ when the starting point is $A$?
I know in $1$-D random walk, like on the vertical line, the probability of an article ever reaches point $B$ when the starting point is $A$ is $\dfrac{p}{q}$ but how to calculate it in $2$-D? Can someone help me please? Thank you!