A factory manufactures an electronic component. Two production lines are used. Production line A produces $40\%$ of the components and production line B produces the rest. Some of the manufactured components have a defect that prevents them from operating at the speed specified by the manufacturer. At the output of line A, $20\%$ of the components have this defect while at the output of line B, only $5\%$ do. A component manufactured in this factory is chosen at random. We denote: A the event ``the component comes from line A'', $B$ the event ``the component comes from line B'', S the event ``the component is defect-free''.

\begin{enumerate}
  \item Show that the probability of event $S$ is $P(S) = 0.89$.
  \item Given that the component has no defect, determine the probability that it comes from line A. The result should be given to the nearest $10^{-2}$.
\end{enumerate}