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14.Probability
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A determinant is chosen at random. The set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that value of the determinant chosen is positive, is
A
$3/16$
B
$3/8$
C
$1/4$
D
None of these
(IIT-1982)
Solution
(a) $n = $ total number of ways $ = {2^4} = 16$
$m = $ Favourable number of ways $ = 3$
Since the value of determinant is positive when it is
$\left| {\,\begin{array}{*{20}{c}}1&0\\0&1\end{array}\,} \right|,\,\,\left| {\,\begin{array}{*{20}{c}}1&0\\1&1\end{array}\,} \right|,\,\,\left| {\,\begin{array}{*{20}{c}}1&1\\0&1\end{array}\,} \right|$.
Hence required probability $ = \frac{3}{{16}}$.
Standard 11
Mathematics
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