If we have two independent brownian motion in $x$ and $y$ direction. At time zero we sit at $(a,b)$ with $a>0, b>0$.

What is the probability that we will hit positive $x$ axis before hitting the negative $x$ axis?

I tried to look at some posts but no clue yet...

https://math.stackexchange.com/questions/88555/2d-brownian-motion-hitting-a-point

2d Brownian motion first passage time

If we have two independent brownian motion in $x$ and $y$ direction. At time zero we sit at $(a,b)$ with $a>0, b>0$.

What is the probability that we will hit positive $x$ axis before hitting the negative $x$ axis?

I tried to look at some posts but no clue yet...

2d-brownian-motion-hitting-a-point

2d Brownian motion first passage time

If we have two independent brownian motion in $x$ and $y$ direction. At time zero we sit at $(a,b)$ with $a>0, b>0$.

What is the probability that we will hit positive x axis before hitting the negative x axis?

I tried to look at some posts but no clue yet...

https://math.stackexchange.com/questions/88555/2d-brownian-motion-hitting-a-point

2d Brownian motion first passage time

If we have two independent brownian motion in $x$ and $y$ direction. At time zero we sit at $(a,b)$ with $a>0, b>0$.

What is the probability that we will hit positive $x$ axis before hitting the negative $x$ axis?

I tried to look at some posts but no clue yet...

https://math.stackexchange.com/questions/88555/2d-brownian-motion-hitting-a-point

2d Brownian motion first passage time