\begin{table}%T4
       \caption{\label{tab_frac}Fraction of Hard X-ray detected EROs.}
%\centerline
{
\begin{tabular}{lccccc}
\hline
\hline
$K$(lim) & $F_{2-10~\rm keV}$(lim) & area & $N$(EROs) & $N$(EROs) & \% \\% & density \\
  & \cgs\ & arcmin$^{2}$ & $K$-selected  & X-ray detected & \\%& arcmin$^{-2}$  \\
\hline
This work: & & & & \\
18.8 &$4 \times10^{-15}$ & $\sim$380 & 173 & 6 & 3.5\% \\
19.2 &$4 \times10^{-15}$ & $\sim$300 & 216 & 7 & 3.2\% \\
all sample & $4\times10^{-15}$ & $\sim$380 & 257 & 9 & $3.5\pm1.2$\% \\
\hline
A02$^{\dag}$: & & & & & \\% &\\
20.1 & $2\times10^{-16}$ & $\sim$70 & 29$^\ddag$ & 4 & 14$^{+11}_{-7}$\% \\
\hline
R03$^{\dag}$: & & & & \\%& \\
21.5 & $4\times10^{-16}$ & $\sim$50 & 179 & 12 & 6.6$^{2.0}_{-1.8}$\% \\
\hline
\end{tabular}}
\smallskip
$^{\dag}$: AO2: Alexander et~al. (\cite{Alexander2002}); R03: Roche et~al.
(\cite{Roche2003}). \\
$^{\ddag}$: Selected on the basis of a $I-K>4$ criterion.
\end{table}