An electron is in a strong, static, homogenous magnetic field with magnitude B0 in the z direction. At time t=0, the spin of the electron is in the +z direction. At t=0 a weak, homogenous magnetic field with magnitude B1 (where B1 << B0) is turned on. At t=0 this field is pointing in the x direction, but it rotates counterclockwise in the x-z plane with angular frequency ω, so that at any later time t this field is at an angle ωt relative to the x-axis:

Calculate the probability that at a later time tf the electron spin has flipped to the -z direction. Do not assume anything about the particular value of ω.