[MCQ/QM-05001] Computing probabilty for outcome of a measurement

1. Find normalized eigenvector of the matrix \(A\) corresponding to the eigenvalue 1. By solving    \[A | 1 \rangle = |1\rangle\]
2. Take scalar product of the eigenvector \(|1\rangle\)  with \(\\psi\rangle\).This means compute \(\langle 1| \psi\rangle \).
3. And then take absolute square of the scalar product. So the answer will be \(\langle 1| \psi\rangle |^2\).

1. Calculation gives \[ |1\rangle =  \frac{1}{\sqrt{2}}\begin{pmatrix} 0 \\ 1\\ -1 \end{pmatrix}\]
2. Scalar product with \(\\langle 1 |\psi \rangle\) = -1/2.
3. So probability is 1/4

Option (d) is the correct answer.