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\large

\centerline{\bf Mercy Hospital}
\centerline{
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline Type & A& B & C & D & E & All \\
\hline Operations & 359 & 1836 & 299 & 2086 & 149 & 4729 \\
\hline Successful & 292 & 1449 & 178 & 434 & 13 & 2366 \\
\hline Rate & 0.81 & 0.79 & 0.60 & 0.21 & 0.09 & 0.50   \\
\hline\end{tabular}
}

\vspace{12pt}

\centerline{\bf Hope Hospital}
\centerline{
\begin{tabular}{|l|c|c|c|c|c|c|}
\hline Type & A & B & C & D & E & All \\
\hline Operations & 88 & 514 & 222 & 86 & 45 & 955 \\
\hline Successful & 70 & 391 & 113 & 12 & 2 & 588 \\
\hline Rate & 0.80 & 0.76 & 0.51 & 0.14 & 0.04 & 0.62 \\
\hline \end{tabular}
}

\vspace{12pt}

\noindent
Fraction of Mercy Hospital's operations that were successful:
\begin{eqnarray*}
0.50 & \approx& \frac{2366}{4729} \\
   &=& \frac{292+1449+178+434+13}{4729} \\
   &\approx& \frac{359(0.81)+1836(0.79)+299(0.60)+2086(0.21)+149(0.09)}{4729} \\
   &=& \frac{359}{4729}(0.81)+\frac{1836}{4729}(0.79)+\frac{299}{4729}(0.60)
      +\frac{2086}{4729}(0.21)+\frac{149}{4729}(0.09)
\end{eqnarray*}

\vspace{12pt}

\noindent
Fraction of all operations that were both successful \underbar{and} done at
Hope:
\begin{eqnarray*}
0.103 &\approx& \frac{588}{4729+955} \\
   &\approx& \frac{4729}{4729+955}(0) + \frac{955}{4729+955}(0.62)
\end{eqnarray*}

\vspace{12pt}

\noindent
Fraction of all successful operations that were done at Mercy:
\begin{eqnarray*}
0.80 &\approx& \frac{2366}{2366+588} \\
   &=& \frac{2366}{2366+588}(1) + \frac{588}{2366+588}(0)
\end{eqnarray*}

\vspace{12pt}

\noindent
Fraction of all Mercy operations that were likely successes (A,B,C):
$$
0.53 \approx \frac{359+1836+299}{4729}
\ (\ = \frac{359}{4729}(1)+\frac{1836}{4729}(1)+\frac{299}{4729}(1)+
\frac{2086}{4729}(0)+\frac{149}{4729}(0)\ )\\
$$

\noindent
Fraction of all Hope operations that were likely successes (A,B,C):
$$
0.86 \approx \frac{88+514+222}{955} \\
$$

\end{document}
