Consider the system of equations where a , b , c , d ∈ { 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

Question

Consider the system of equations where a , b , c , d ∈ { 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 .

TestHub · Accepted Answer

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.

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