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
$=\begin{bmatrix}1 & 0 \\ 1 & 1\end{bmatrix},\begin{bmatrix}1 & 1 \\ 0 & 1\end{bmatrix},\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix},\begin{bmatrix}0 & 1 \\ 1 & 0\end{bmatrix},\begin{bmatrix}1 & 1 \\ 1 & 0\end{bmatrix},\begin{bmatrix}0 & 1 \\ 1 & 1\end{bmatrix}$
$\therefore P ($ singular $)=1- P ($ Non-Singular $)=1-\frac{6}{16}=\frac{5}{8}$.