  The observations of compact star inspirals from LIGO/Virgo provide a valuable
tool to study the highly uncertain equation of state (EOS) of dense matter at
the densities in which the compact stars reside. It is not clear whether the
merging stars are neutron stars or quark stars containing self-bound quark
matter. In this work, we explore the allowed bag-model-like EOSs by assuming
the merging stars are strange quark stars (SQSs) from a Bayesian analysis
employing the tidal deformability observational data of the GW170817 and
GW190425 binary mergers. We consider two extreme states of strange quark
matter, either in nonsuperfluid or color-flavor locked (CFL) and find the
results in these two cases essentially reconcile. In particular, our results
indicate that the sound speed in the SQS matter is approximately a constant
close to the conformal limit of $c/\sqrt{3}$. The universal relations between
the mass, the tidal deformability and the compactness are provided for the
SQSs. The most probable values of the maximum mass are found to be $M_{\rm
TOV}=2.10_{-0.12}^{+0.12}~(2.15_{-0.14}^{+0.16})\,M_{\odot}$ for normal (CFL)
SQSs at a $90\%$ confidence level. The corresponding radius and tidal
deformability for a $1.4\,M_{\odot}$ star are $R_{\rm 1.4}=
11.50_{-0.55}^{+0.52}~({11.42}_{-0.44}^{+0.52})~\rm km$ and $\Lambda_{1.4}=
{650}_{-190}^{+230}~({630}_{-150}^{+220})$, respectively. We also investigate
the possibility of GW190814's secondary component $m_2$ of mass
$2.59_{-0.09}^{+0.08}\,M_{\odot}$ being an SQS, and find that it could be a CFL
SQS with the pairing gap $\Delta$ larger than $244~\rm MeV$ and the effective
bag parameter $B_{\rm eff}^{1/4}$ in the range of $170$ to $192$ MeV, at a
$90\%$ confidence level.
