Question

A $2\times 2$ matrix is formed with entries from the set $\{0,1\}$. The probability that it is singular, is

• A. $\frac{3}{8}$
• B. $\frac{1}{8}$
• C. $\frac{5}{8}$
• D. $\frac{5}{16}$

Answer 1

Answer: (C)

Number of non singular determinant
$=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right],\left[\begin{array}{cc}1& 1\\ 0& 1\end{array}\right],\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right],\left[\begin{array}{cc}1& 1\\ 1& 0\end{array}\right],\left[\begin{array}{cc}0& 1\\ 1& 1\end{array}\right]$
$\therefore P($ singular $)=1-P($ Non-Singular $)=1-\frac{6}{16}=\frac{5}{8}$.