Undergrad Possible simple Density Matrix Question

[Diracobama2181]

If I am given that the density matrix of an incoming beam of spin 1 particles of the form $$p_o=(1/3)[|1><1|+|0><0|+|-1><-1|]$$, aand I needed to find the fraction of particles that would be found with a spin x component of zero, how would I go about solving this problem?
My hunch is that I would just use $$trace(p_o|0>_x<0|_x)$$, where $$|0>_x$$ is written in terms of the z component. Is this correct?

 

[vanhees71]

That's correct, but first think about, how to simplify your statistical operator!