If A and B are events then the value of the determinant chosen at random from all the determinants of order 2 with entries 0 or 1 only is positive and negative respectively, then:
Answer & explanation
Correct answer: option 4
Positive value of determinant :$\begin{vmatrix}1&0\\0&1\end{vmatrix},\begin{vmatrix}1&0\\1&1\end{vmatrix},\begin{vmatrix}1&1\\0&1\end{vmatrix}$; Negative value of determinant :$\begin{vmatrix}0&1\\1&0\end{vmatrix},\begin{vmatrix}0&1\\1&1\end{vmatrix},\begin{vmatrix}1&1\\1&0\end{vmatrix}$
Total possible outcomes = 24 = 1 ⇒ P(A) = 3/16 ; P(B) = 3/16