Question

If each element of a second order determinant is either zero or one , then the probability that value of the determinant is negative is

• A. $\frac{13}{16}$
• B. $\frac{3}{16}$
• C. $\frac{3}{13}$
• D. $\frac{11}{16}$

Answer 1

The correct option is B $\frac{3}{16}$

Total no. of possible determinant $2^4=16$
Total no. of determinant having negative value =$3$
$\left|\begin{array}{cc}1& 1\\ 1& 0\end{array}\right|,\left|\begin{array}{cc}0& 1\\ 1& 1\end{array}\right|,\left|\begin{array}{cc}0& 1\\ 1& 0\end{array}\right|$
probability=$\frac{3}{16}$