Hi,
If you computed the four possible outcomes, you have computed the projection P |psi> where
P is the appropriate projector and |psi> the initial state.
The probability of this outcome is then <psi| P |psi>.
Note that since P^2=P for a projector this is also equal to <psi| P^2|psi> and so it suffices to compute the norm of P|psi>.
Hope this clarifies
