A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 o

Question

A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the value of determinant chosen is positive is m/n. m+n=?

Professor PC Thomas Classes · Answer

With 0 and 1 as elements there are $2 	imes 2$ $	imes 2 	imes 2=16$ determinants of order $2 	imes 2$ out of which only\ $\left|\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight|,\left|\begin{array}{ll}1 & 1 \ 0 & 1\end{array}ight|,\left|\begin{array}{ll}1 & 0 \ 1 & 1\end{array}ight|$ are the three\ determinants whose value is +ve .\ $	herefore \quad$ Req. prob. $=3 / 16$\