A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is negative is

determinants are

$$\begin{gathered} \left|\begin{array}{cc}0& 0\\ 0& 0\end{array}\right| \left|\begin{array}{cc}0& 0\\ 0& 1\end{array}\right| \left|\begin{array}{cc}0& 0\\ 1& 0\end{array}\right| \left|\begin{array}{cc}0& 1\\ 0& 0\end{array}\right| \left|\begin{array}{cc}1& 0\\ 0& 0\end{array}\right| \left|\begin{array}{cc}1& 1\\ 0& 0\end{array}\right| \left|\begin{array}{cc}0& 0\\ 1& 1\end{array}\right| \left|\begin{array}{cc}1& 0\\ 1& 0\end{array}\right| \\ \left|\begin{array}{cc}0& 1\\ 0& 1\end{array}\right| \left|\begin{array}{cc}1& 0\\ 0& 1\end{array}\right| \left|\begin{array}{cc}0& 1\\ 1& 0\end{array}\right| \left|\begin{array}{cc}1& 1\\ 1& 0\end{array}\right| \left|\begin{array}{cc}1& 0\\ 1& 1\end{array}\right| \left|\begin{array}{cc}0& 1\\ 1& 1\end{array}\right| \left|\begin{array}{cc}1& 1\\ 0& 1\end{array}\right| \left|\begin{array}{cc}1& 1\\ 1& 1\end{array}\right| \end{gathered}$$

$\mathrm{n}\left(\mathrm{S}\right)=16$    E= det value is negative

$\mathrm{n}\left(\mathrm{E}\right)=3 \Rightarrow \mathrm{P}\left(\mathrm{E}\right)=\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$6$}\right.$