1.
\[
P(A|BC) = \frac{P(AB|C)}{P(B|C)}
\]
2.
In EM algorithm, the usual expectation function can be written as follows:
\[
\begin{split}
Q(\theta,\theta^0) &= E_{h}\left[P(\mathbf{x},h|\theta)|\mathbf{x},\theta^0\right] \\
& = \sum_{h}P(\mathbf{x},h|\theta)P(h|\mathbf{x},\theta^0)
\end{split}
\]
where
$h$ : the hidden varible.
$\theta$ : the obvious varible.
$\mathbf{x}$ : the observed data.
$\theta^0$ : the obvious varible calculated on the last.