A drunkard performs a brisk walk and takes a step forward with the probability of 0.3 followed by a step backwards and so on. What is the probability that at the end of 13th step he is one step away from the initial position

Dear student

hi Arun. I have a question. You assumed the probability of taking a step backwards = 1 – 0.3 = 0.7. This implies that you ignored the possibility that he doesn’t move at all. You assumed that 1 = P(forward step) + P(backward step). But ideally, it should be 1 = P(forward step) + P(backward step) + P(no step at all).