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# A determinant is chosen at random from the set of all determinants of order 2 with elements 0 and 1 only. The probability that the determinant chosen is non-zero is

$\begin {array} {1 1} (A)\;\large\frac{3}{16} & \quad (B)\;\large\frac{3}{8} \\ (C)\;\large\frac{1}{4} & \quad (D)\;None\: of\: these \end {array}$

Total number of determinants = $2^4$
$= 16$
$\begin {vmatrix} 1 & 1 \\ 0 & 1 \end {vmatrix}$, $\begin {vmatrix} 1 & 0 \\ 1 & 1 \end {vmatrix}$, $\begin {vmatrix} 1 & 0 \\ 0 & 1 \end {vmatrix}$,$\begin {vmatrix} 1 & 1 \\ 1 & 0 \end {vmatrix}$,$\begin {vmatrix} 0 & 1 \\ 1 & 1 \end {vmatrix}$,$\begin {vmatrix} 0 & 1 \\ 1 & 0 \end {vmatrix}$
$\therefore$ Required probability = $\large\frac{6}{16} = \large\frac{3}{8}$