A company packages white sugar from two farms $U$ and $V$ in 1 kg packets. We admit that $3\%$ of the sugar from farm $U$ is extra fine and that $5\%$ of the sugar from farm V is extra fine. A packet of sugar is randomly selected from the company's production and we consider the following events:
\begin{itemize}
  \item $U$: ``The packet contains sugar from farm U'';
  \item $V$: ``The packet contains sugar from farm V'';
  \item $E$: ``The packet bears the label `extra fine' ''.
\end{itemize}

\begin{enumerate}
  \item In this question, we admit that the company manufactures $30\%$ of its packets with sugar from farm U and the others with sugar from farm V, without mixing sugars from the two farms.\\
a. What is the probability that the selected packet bears the label ``extra fine''?\\
b. Given that a packet bears the label ``extra fine'', what is the probability that the sugar it contains comes from farm U?
  \item The company wishes to modify its supply from the two farms so that among the packets bearing the label ``extra fine'', $30\%$ of them contain sugar from farm U. How should it supply itself from farms U and V? Any working will be valued in this question.
\end{enumerate}