Probability of Hitting Vertical vs Horizontal Lines in 2D Grid

[iamback]

Hi, I have a problem

(1) where I need to compute the ratio of probabilities of hitting and stopping at a positive vertical barrier x vs hitting and stopping at a negative horizontal barrier y after starting from (0,0).

I feel that by symmetry, the answer to this would be the same as

(2) The probability of hitting -y vs hitting +x, horizontal lines in 2d grid,

which looks like being same as

(3) The probability of hitting -y vs x on a real line.

Can someone please tell me if my 1->2 assumption or 2->3 assumption is wrong. In which case, could someone please tell me how to proceed with the solution to 1.

However, if my assumption is right, can someone tell me how to proceed to prove it. Also, what would be a way to solve the case when both x and y are positive.



I shall be grateful for a response/hint/link.

Thanks.
PS: Please note that this is NOT a homework question and I really want to see this problem from a conceptual perspective. I've asked this question of many people, but none seem to be able to answer it.

 

[bpet]

I think the issue is that (1) can be interpreted several ways. Could you provide more detail?