Find the matrices $S_i$, $i = x, y, z$ representing the spin of a particle with $s = 5/2$ (for example, here: https://www.easyspin.org/documentation/spinoperators.html)
(a) The particle is in an eigenstate $|5/2, 5/2\rangle$ of $S_x$. What is the probability to measure $S_z = |5/2, -1/2\rangle$.
(b) The particle is in an eigenstate $|5/2, -1/2\rangle$ of $S_x$. What are the most probable values upon a measurement of $S_z$?