Relation b/w probability of triplet state and singlet state

[wishfulthinking]

Homework Statement

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If electron (1) is in a state described by cosα1χ+ + sinα1e iβ1 χ- and electron (2) is in a state described by cosα2χ+ + sinα2e iβ2 χ-, what is the probability that the two-electron state is in a triplet state?

The Attempt at a Solution

I already solved this problem; I have a conceptual question about solving it using a relation that would make my solution a lot simpler. I read somewhere online that the probability of finding the electron system in the triplet state can be equated to (1 - the probability of finding the electron system in the singlet state). I was wondering how this is possible. Thanks for any input.

 

[blue_leaf77]

The space consisting of two angular momenta each equal to ##1/2## is a 4 dimensional space - it is spanned by 4 basis vectors. 3 of them belongs to the triplet state and the last one belongs to the singlet state. The point here is that, for two ##1/2## angular momenta, there can only be triplet or singlet. That's why the probability of finding triplet states is equal to unity minus the probability of finding a singlet state.