Solution
= Solution
\b[False.] For every deterministic $t>0$, <Brownian scaling> gives $B_t/\sqrt t\sim N(0,1)$. In particular, for any $\varepsilon>0$,
$$
\mathbb P(|B_t|/\sqrt t>\varepsilon)=2\bigl(1-\Phi(\varepsilon)\bigr)>0,
$$
independently of $t$. Almost-sure convergence would imply <convergence in probability>, but these fixed positive tail probabilities rule out convergence in <probability> to zero. The square-root normalization retains fluctuations of order one.