Question

Consider the system of equations $a x+b y=0, c x+d y=0$, where $a, b, c, d \in\{0,1\}$
STATEMENT - 1: The probability that the system of equations has a unique solution is $3 / 8$.
and
STATEMENT -2 : The probability that the system of equations has a solution is 1 .

• A. Statement-1 is True, Statement -2 is True; Statement- 2 is a correct explanation for Statement-1
• B. Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1
• C. Statement -1 is True, Statement -2 is False
• D. Statement -1 is False, Statement -2 is True

Answer 1

Answer: (B)

For unique solution $\begin{vmatrix} a & b \\ c & d \end{vmatrix} \neq 0$ where $a , b , c , d \in\{0,1\}$
Total cases $=16$
Favorable cases $=6$
(Either ad $=1, bc =0$ or $ad =0, bc =1)$
Probability that system of equations has unique solution is
$\frac{6}{16}=\frac{3}{8}$
and system of equations has either unique solution or infinite solutions so that probability for system to have a solution is $1$ .