14.Probability
medium

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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