Measuring an Electron Spin

A electron spin in quantum mechanics is given by the superposition state:

\[\large |\Psi\rangle = \frac{i}{2} |\uparrow\rangle + \dfrac{\sqrt{3}}{2} |\downarrow\rangle.\]

What is the probability of measuring the spin in the \(z\)-direction to have value equal to \(-\dfrac{\hbar}{2}\)?

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