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In the following sub-questions we will attempt to solve the problem with only partial observations. That is, we only have access to $\{(x^{(i)}, y^{(i)})\}_{i=1}^n$, and will try to predict $p(t^{(i)}=1 | x^{(i)})$.

\item \subquestionpoints{5} \textbf{Warm-up with Bayes rule}

Show that under our assumptions, for any $i$, 
\begin{align}
p(t^{(i)}=1\mid y^{(i)} = 1, x^{(i)}) = 1
\end{align}
That is, observing a positive partial label $y^{(i)}=1$ tells us for sure the hidden true label is 1. Use Bayes rule to derive this (an informal explanation will not earn credit).