Question

Consider the system of equations ax + by = 0, cx + dy = 0 where a, b, c, d $\epsilon$ {0, 1}. The probability that the system of equations has unique solution is

• A. 3/16
• B. 3/8
• C. 5/8
• D. 5/16

Answer 1

The correct option is B

3/8

For unique solution,

$\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|$ $\ne$0

n(s) = $2^4$ = 16

ad – bc$\ne$ 0 $\Rightarrow$ ad $\ne$bc

∴ad = 1, bc = 0 (or) ad = 0, bc = 1

∴n(E) = 6

P(E) =$\frac{6}{16}$ = $\frac{3}{8}$