A technician controls the machines equipping a large company. All these machines are identical. We know that:
\begin{itemize}
  \item $20\%$ of machines are under warranty;
  \item $0.2\%$ of machines are both defective and under warranty;
  \item $8.2\%$ of machines are defective.
\end{itemize}
The technician tests a machine at random. We consider the following events:
\begin{itemize}
  \item G: ``the machine is under warranty'';
  \item $D$: ``the machine is defective'';
  \item $\bar{G}$ and $\bar{D}$ denote respectively the complementary events of $G$ and $D$.
\end{itemize}

The machine is defective. The probability that it is under warranty is approximately equal, to $10^{-3}$ near, to:\\
a. 0.01\\
b. 0.024\\
c. 0.082\\
d. 0.1