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If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability $1 / 2$
If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability $1 / 2$
CBSE | Class 12 | Maths | NCERT | Probability
If each element of a second order determinant is either zero or one, what is the probability that the value of the determinant is positive? (Assume that the individual entries of the determinant are chosen independently, each value being assumed with probability $1 / 2$

Solution:

We can deduce the following information from the question:

The total number of determinants of second order in which the element is or is not $1=(2)^{4}$ $=16$

Now, we have the value of determinants is positive in following cases:

$\left|\begin{array}{ll|ll|l|}1 & 0 & 1 & 11 & 0 \ 0 & 1 & 0 & 11 & 1\end{array}\right|$

$\therefore$ Required probability $=3 / 16$

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