= Solution
The <probability current> is
$$
j=\frac{\hbar}{2mi}\left(\psi^*\psi'-\psi\psi^{*\prime}\right)=\frac\hbar m\operatorname{Im}(\psi^*\psi').
$$
For the incident and transmitted travelling waves, $j_{\rm in}=\hbar k|A|^2/m$ and $j_{\rm tr}=\hbar k|F|^2/m$. Thus \b[$P(E)=|F/A|^2$] here. If the asymptotic wave numbers differed, the ratio of outgoing to incoming velocities would also be required. Current conservation gives $P+|B/A|^2=1$ for a real nonabsorbing barrier.
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