Probabilistic Turing machine – Probability that the head has moved k steps to the right on the work tape


I have a PTM with following transition:

$ \delta(Z_0, \square , 0) = \delta(Z_0, \square , L, R)$ ,

$ \delta(Z_0, \square , 1) = \delta(Z_0, \square , R, R)$

Suppose that this PTM executes n steps. What is the probability that the head has moved k steps to the right on the work tape (in total, i.e., k is the difference between moves to the right and moves to the left) ?