You place a token at the origin (0, 0) of the square grid. You move token from one vertex to the neighboring vertex so that with probability 1/2 you move the token one vertex up and with probability 1/2 you move the token one vertex to the right. In other words, if at some point the token is at (x, y) in the next move it will be at (x, y + 1) with probability 1/2 or at (x + 1, y) with probability 1/2. Each time you move the token independently of all other moves. You stop when you hit the wall placed along the line x = k which is perpendicular to the x axis and parallel to the y axis. Let (k, Y ) be the final position of the token when it hits the wall. Compute the probability P(Y = n) for any integer n ≥ 0.
You place a token at the origin (0, 0) of the square grid. You move token from one vertex to the neighboring vertex so that with probability 1/2 you move the token one vertex up and with probability 1/2 you move the token one vertex to the right. In other words, if at some point the token is at (x, y) in the next move it will be at (x, y + 1) with probability 1/2 or at (x + 1, y) with probability 1/2. Each time you move the token independently of all other moves. You stop when you hit the wall placed along the line x = k which is perpendicular to the x axis and parallel to the y axis. Let (k, Y ) be the final position of the token when it hits the wall.
Compute the probability P(Y = n) for any integer n ≥ 0.
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