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Probabilities for components of spin angular momentum

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I'll denote spin in the +z direction by (1,0) and in the -z direction by (0,1).

In Quantum Mechanics, if a particle is in some state |p> the probability that after some measurement you find that this particle in some state |q> is given by the absolute value squared of the inner product:

|<q|p>|^2

So, if the normalized spin wavefunction is (psi1, psi2), then that means that when you measure the z-component of the spin, the probability that you find that the spin is in the +z direction is:

|(psi1, psi2) dot (1,0)|^2 = |psi1|^2

Here ...

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