For any language $L \subseteq \mathbb{B^{*}}$ we define language $2 \cdot L$ as set $\{2 \cdot \overline{a} | \overline{a} \in L\}$, where $2$ in binary form equals $10$,and $\cdot$ - is multiplication of two binary numbers.
Prove:
if $L \in \mathbf{BPP}$, then $2 \cdot L \in \mathbf{BPP}$.
I know how to show it for not probabilistic Turing machine. Its just simple Turing machine for multiplication of two binary numbers. I dont know how to show it with probability and I stuck here.