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## Homework Statement

Consider two spin 1/2 particles. Initially these two particles are in a spin singlet state. If a measurement shows that particle 1 is in the eigenstate of ##S_x = -\hbar/2##, what is the probability that particle 2 in this same measurement is in the eigenstate of ##S_z = \hbar/2##?

## Homework Equations

##\chi^{(x)}_{\pm} = \begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{\pm1}{\sqrt{2}}\end{pmatrix}## and

##\chi^{(z)}_{+} = \begin{pmatrix}1\\0\end{pmatrix}##

##\chi^{(z)}_{-} = \begin{pmatrix}0\\1\end{pmatrix}##

## The Attempt at a Solution

Okay so I am not entirely sure how to proceed, my instinct tells me to setup a linear combination of two measurements such that the linear combo is equal to one, i.e.:

$$

\begin{pmatrix}1\\1\end{pmatrix} = a

\begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{-1}{\sqrt{2}}\end{pmatrix} + b \begin{pmatrix}1\\0\end{pmatrix}

$$ But that gives a or b =1. So that is not correct. What am i doing wrong?