Likelihood P(d < R) of non-detection of binary (left) or planetary mass (right) companions within the cavity of a set of observed transition discs as a function of radius under the hypothesis that companions caus the cavity to form (obtained as described in Sect. 4.2.2). For each system, the plot shows two curves that are joined by a colour-shaded area. The solid curve is associated with the optimistic ($q_{\text{max}}^{+}$, Eq. (8)) companion detection limits, and the dotted curve is associated with the conservative ($q_{\text{max}}^{-}$, Eq. (9)) companion detection limits. The colour-shaded area is a confidence interval between the two upper limits of the mass ratio. The end of each line marks the location of the cavity edge $R=a_{\text{cav}}^{\text{obs}}$. Under the assumption that a companion forms the cavity, P(d < R) represents the likelihood that a companion with a projected separation d < R remains undetected in the disc cavity. For example, for the system CQ Tau, assuming a companion is carving the observed cavity, P(d < R = 0.2) ∼ 80% represents the likelihood that it goes undetected if it has projected separation d < 0.2 arcsec. The value of $P(d<R=a_{\mathrm{c}\mathrm{a}\mathrm{v}}^{\text{obs}})$, that is the value of P at the end of each line, represents the total likelihood in the whole cavity area. We label the total likelihood for the conservative and optimistic upper limits of binaries and planets as ${\mathcal{L}}_{\text{bin}}^{\pm }$ and ${\mathcal{L}}_{\text{pl}}^{\pm }$, respectively, and report them in Table 2. Additional discussion can be found in Sect. 5. As discussed in Sect. 4.2, we remark that a low likelihood allows us to exclude our hypothesis that a companion is responsible for the cavity; in contrast, a high likelihood does not mean that a companion is expected to be found in the cavity, but that under the hypothesis a companion is there carving the cavity high are the chances it goes undetected.