# The Random Walk

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Consider a one dimensional random walk performing discrete jumps of length $a$ at each time step.

a) Calculate $P(p,N)$ the probability that the walk of $N$ steps performs $p$ steps to the right.

I do not know if the binomial probability approach can be applied to this problem. If that is the case, why?

The information I used:

edited Oct 16, 2018
It is about the approach Sr. Please see my question again, I updated it.
Why shouldn't the binomial probability approach apply here? There are only 2 choices at each step, and these are determined by probability.

I would suggest that you post this question in Mathematics SE. However I think it would be closed as "Not clear what you are asking".

Whether there is any physical insight which would make this problem easier to solve, I do not know.

1 vote

The walker takes a series of steps. At each step he has only 2 choices : move left or move right. Which he chooses is determined completely at random and each has a definite probability. Note that it is not necessary for the probabilities to be equal, but they must add up to $1$ - ie these must be the only 2 outcomes which are possible, and they must be mutually exclusive.
This is exactly equivalent to tossing a coin $N$ times. Instead of $H, T$ you have $R, L$. The position of the walker on the line of integers is equivalent to the number of heads minus the number of tails.