I am solving the following:
Let $W_t$ be a one-dimensional brownian motion on $(\Omega,F,P)$. Prove that for any constants $a,b >0$ there exists $A \in F$ such that $P(A)=1$ and a function $t(\omega)$ such that $inf_{s \ge t(\omega)}(as+bW_{s}(\omega)) \ge 0.$
I honestly have no idea how to approach this problem. I think I might be able to use the quadratic variation of the process but I'm not sure how.