= Solution
For nonzero <Rabi detuning>,
$$
\boxed{P_-(t)=\frac{\gamma^2}{\gamma^2+\Omega^2}\sin^2\left(\sqrt{\gamma^2+\Omega^2}\,t\right).}
$$
The sketch starts at zero and oscillates between zero and $\gamma^2/(\gamma^2+\Omega^2)<1$, with <period> $\pi/\sqrt{\gamma^2+\Omega^2}$ when the coupling is nonzero. Relative to resonance, the oscillations have a smaller maximum and a shorter <period> at fixed coupling. The sign of the <Rabi detuning> changes the amplitudes' <phases> but leaves this <transition probability> unchanged. For $|\Omega|\gg|\gamma|$, its maximum is approximately $\gamma^2/\Omega^2$, so population transfer is strongly suppressed. The plotted detuned example has $|\Omega|=|\gamma|$, giving maximum $1/2$.
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