question about brownian motion hitting a point 'a'

[vkaul]

I just wanted to know how to solve the problem of calculating the probability of a Brownian motion hitting point a that is positive before point b that is negative. Can we solve it using a random walk itself or there is a better way?

 

[Stefan Zota]

Yes BM is a scaled random walk (by contruction). Initially you can make simplifying assumptions and deal only with random walks.
Another important notion is the reflection principle. In your problem, once you reach point 'a', there is an equal number of paths to reach 'b' and '2a - b' ...