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 GW190814s 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.
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