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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Probability
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Q)

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

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

 

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A)
Total number of determinants = $ 2^4$
$ = 16$
Determinants with positive and negative values are
$ \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}$
Ans : (B)
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