# 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) ?