\begin{table}%T9
%\centering
\small
  \caption{The observed binary fraction (in \%) and inferred intrinsic binary fraction (in \%) for the different datasets discussed in this paper. Columns~1 and~2 list the dataset and the observed binary fraction. The predicted observed binary fraction resulting from \"{O}pik's law for each dataset (adopting $\binfrac=100\%$) is listed in Col.~3, followed by the inferred $1\sigma$, $2\sigma$ and $3\sigma$ confidence ranges of the inferred binary fraction. The predicted observed binary fraction for the log-normal period distribution with $\mu=4.8$ and $\sigma=2.3$ (adopting $\binfrac=100\%$) and corresponding confidence ranges for the intrinsic binary fraction are listed in Cols.~7--10. The adopted association parameters are listed in Table~\ref{table: subgroups}. For models in Cols.~3--6 the semi-major axis range is $5\rsun \leq a \leq 5\times 10^6 \rsun$.  For models in Cols.~7--10 the period range is $0.7~\mbox{day} \leq P \leq 3\times 10^8~\mbox{day}$. For each model we assume a mass ratio distribution of the form $f_q(q) \propto q^\gamma_q$ with $\gamma_q=-0.4$ and a thermal eccentricity distribution. The comparison between observations and simulated observations indicates that the binary fraction among intermediate-mass binaries in \sco{} is close to 100\% ($\protect\ga $70\% with $3\sigma$ confidence).   
    \label{table: fm_inferred} }
  \begin{tabular}{lrrcccrccc}
    \hline
    \hline
    Dataset & \multicolumn{1}{c}{Obs.}  & \multicolumn{4}{c}{$f_{\gamma_a}(a)$, $\gamma_a=-1$}     & \multicolumn{4}{c}{$f_{\mu,~\sigma}(P)$, $\mu=4.8$, $\sigma=2.3$}   \\
    \hline\\[-3.2mm]
    & \multicolumn{1}{c}{$\binfracobs$} 
    & \multicolumn{1}{c}{$\binfracobs$} & $\binfrac$$(1\sigma)$ & $\binfrac$$(2\sigma)$ & $\binfrac$$(3\sigma)$ 
    & \multicolumn{1}{c}{$\binfracobs$} & $\binfrac$$(1\sigma)$ & $\binfrac$$(2\sigma)$ & $\binfrac$$(3\sigma)$ \\
    \hline  
    KO5                  & $30\pm4$      & 26     & $\approx $100 & $91$--$100$ & $81$--$100$ & 35    & $97$--$100$ & $70$--$100$ & $61$--$100$ \\
    KO6                  & ${<}82\pm8$     & 27     & $\dots$ & $\dots$ & $\dots$         & 37    & $\dots$ & $\dots$ & $\dots$ \\
    SHT                  & $26\pm4$      & 23     & $94$--$100$ & $77$--$100$ & $63$--$100$      & 34    & $64$--$97$ & $52$--$100$ & $43$--$100$ \\
    \hline
    LEV SB1/SB2 only     & ${>}30\pm6$     & 36     & ${>}68$ & ${>}54$ & ${>}42$               & 24    & $\approx $100 & ${>}81$ & ${>}64$ \\
    LEV SB1/SB2/RVV      & ${<}74\pm6$     & 36     & $\dots$ & $\dots$ & $\dots$         & 24    & $\dots$ & $\dots$ & $\dots$ \\
    BRV analysis -- RVV  & ${<}60\pm5$     & 39     & $\dots$ & $\dots$ & $\dots$         & 27    & $\dots$ & $\dots$ & $\dots$ \\
    BRV SB1/SB2/RVV      & ${<}66\pm5$     & 39     & $\dots$ & $\dots$ & $\dots$         & 27    & $\dots$ & $\dots$ & $\dots$ \\
    \hline
    HIP (X)/(O)/(G)      & $4\pm1$       & ${<}31$  & ${>}12$ & ${>}10$ & ${>}8$                & ${<}25$ & ${>}14$ & ${>}11$ & ${>}9$ \\
    HIP (X)/(O)/(G)/(S)  & $9\pm1$       & ${<}31$  & ${>}25$ & ${>}22$ & ${>}19$               & ${<}25$ & ${>}30$ & ${>}26$ & ${>}22$ \\
    HIP (C)              & $15\pm2$      & 13     & $\approx $100 & $96$--$100$ & $86$--$100$ & 18    & $77$--$94$ & $68$--$100$ & $61$--$100$ \\
    \hline
  \end{tabular}
\end{table}