i'm trying to do this exercise on Markov Chain
A bidimensional Random Walk in the discrete time moves on step in one of the four directions North, South, East, West with probability respectively equal to p,p,q,q. Axis are reflective barriers so that the walk only occurs in the first quadrant(X and Y non-negative integers). Denoted by (i,j) the state, i.e the position of the walk.
Find the distribution of the walk on the horizontal line.
Now my question is about the draw of the scheme: supposing that in the origin of the axis i have the state(0,0). Then i will move to the right( state (0,1)) with probability 1( i have a reflective barrier). But how about state (1,0) ? I cannot move upward since the sum will be 1+1=2, and it cannot be since we are talking about probability. Anyone could help me ?