Question

A determinant is chosen at random from the set of determinants of order 2 with elements 0 and 1. What is the probability that the determinant chosen has the value non-negative?

• A. 3/16
• B. 10/16
• C. 13/16
• D. 6/16

Answer 1

The correct option is C

13/16

1-P (Determinant has a negative value) = $1-\frac{3}{16}$

$\left|\begin{array}{cc}0& 1\\ 1& 1\end{array}\right|$,

$\left|\begin{array}{cc}0& 1\\ 1& 0\end{array}\right|$

$\left|\begin{array}{cc}1& 1\\ 1& 0\end{array}\right|$,

for each place there are 2 cases. Total possible cases: 16 $P=1-\frac{3}{16}=\frac{13}{16}$