Solution:
We can deduce the following information from the question:
The total number of determinants of second order in which the element is or is not $1=(2)^{4}$ $=16$
Now, we have the value of determinants is positive in following cases:
$\left|\begin{array}{ll|ll|l|}1 & 0 & 1 & 11 & 0 \ 0 & 1 & 0 & 11 & 1\end{array}\right|$
$\therefore$ Required probability $=3 / 16$