Table 9: 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 Öpik's law for each dataset (adopting $F_{M}=100\%$) 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 $F_{M}=100\%$) and corresponding confidence ranges for the intrinsic binary fraction are listed in Cols. 7-10. The adopted association parameters are listed in Table 1. For models in Cols. 3-6 the semi-major axis range is $5~{R}_\odot\leq a \leq 5\times 10^6 ~{R}_\odot$. 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 OB2 is close to 100% ( $\protect\ga $70% with $3\sigma $ confidence).
Dataset Obs. $f_{\gamma_a}(a)$, $\gamma_a=-1$ $f_{\mu,~\sigma}(P)$, $\mu =4.8$, $\sigma =2.3$
  $\tilde{F}_{M}$ $\tilde{F}_{M}$ FM$(1\sigma)$ FM$(2\sigma)$ FM$(3\sigma)$ $\tilde{F}_{M}$ FM$(1\sigma)$ FM$(2\sigma)$ FM$(3\sigma)$
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
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 $\dots$ $\dots$ $\dots$
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

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