$W_{t}$ is a Wiener process.
I've spent a couple hours trying to solve that. I thought that Bachelier theorem can be applied here, but I'm not sure how exactly. Or maybe some other technique is at use here.
Maybe there is some martingale and stopping moment here, so I can use Dub's theorem.
Bachelier theorem: $\forall$ T and $x \geq 0$ $P (max W(t) \geq x) = 2P(W(T) \geq x)=P(|W(T)|\geq x)$.