Question

Consider the system of equations $ax+$ by $=0,cx+dy=0$, where $a,b,c,d\in \{0,1\}$.

STATEMENT--1: The probability that the system of equations has a unique solution is $3/8$
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)

Statement -1 is True, Statement -2 is True; Statement-2 is NOT a correct explanation for Statement-1

For unique solution $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|\ne 0$ 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 $1$
Hence, option 'B' is correct.