Consider the system of equations where $\quad a, b, c, d \in\{0,1\}$ 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.
• Correct answer
  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

Solution

The number of all possible deteminants of the form
Out of which only 10 determinants given by
vanish and remaining six determinants have non-zero values. Hence, the required probability $=\frac{6}{16}=\frac{3}{8}$ $\Rightarrow$ Statement 1 is correct. Statement 2 is also correct as the homogeneous equations have always a solution and Statement 2 is not a correct explanation of Statement 1.

Hence, the correct answer is option: 'B'.