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:<math>
\begin{matrixalign}
\mathbb{P}(x \mbox{ received} \mid y \mbox{ sent}) & ={} &= \frac{ \mathbb{P}(x \mbox{ received} , y \mbox{ sent}) }{\mathbb{P}(y \mbox{ sent} )} \\
& ={} &= \frac{ \mathbb{P}(x \mbox{ received} , y \mbox{ sent}) }{\mathbb{P}(y \mbox{ sent})} \frac{\mathbb{P}(y \mbox{ sent})}{\mathbb{P}(x \mbox{ sent})} \\ ▼&& \\
& ={} &= \frac{ \mathbb{P}(x \mbox{ received} , y \mbox{ sent}) }{\mathbb{P}(y \mbox{ sent})} \frac\
& {} = \mathbb{P}(y \mbox{ sentreceived})}{ \mathbb{P}(mid x \mbox{ sent})} \\.
&& \\
▲& = & \frac{ \mathbb{P}(x \mbox{ received} , y \mbox{ sent}) }{\mathbb{P}(y \mbox{ sent})} \\
&& \\
& = & \mathbb{P}(y \mbox{ received} \mid x \mbox{ sent}) \\
</math>
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