A beam of spin-1/2 particles moving along the y axis goes through two collinear SG apparatuses, both with lower beams blocked. The first has its B field along the z axis and the second has its B field along the x axis (i.e., is obtained by rotating the first by an angle π/2 about the y axis). What fraction of particles leaving the first will exit the second? If a third filter that transmits only spin up along the z axis is introduced, what fraction of particles leaving the first will exit the third? If the middle filter transmits both spins up and down (no blocking) the x axis, but the last one transmits only spin down the z axis, what fraction of particles leaving the first will leave the last?