Question

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

Answer 1

Answer: (A)

3/16

Answer 2

$n =$ Total number of ways $= 2 ^ { 4 } = 16$

$m =$ Favourable number of ways

Since the value of determinant is positive when it is

$\left| \begin{array} { l l } 1 & 0 \\ 0 & 1 \end{array} \right| , \left| \begin{array} { l l } 1 & 0 \\ 1 & 1 \end{array} \right| , \left| \begin{array} { l l } 1 & 1 \\ 0 & 1 \end{array} \right|$ . Hence required probability $= \frac { 3 } { 16 }$