Chance alignment. Upper panel: The cumulative distribution of expected random (unrelated) X-ray detections from forced photometry using a circular aperture of radius 30″ around 1604 optical quasar candidate positions. The black curve is the estimate obtained from Eq. (2). for a single eRASS survey. The black dashed curve shows an empirical estimate of the same number based on a random sample of positions in the surveyed field. The brown curve shows the number of expected contaminants obtained from a random sample in eRASS:4. Blue vertical lines indicate the P_b values of the best detection of quasars discovered in this work in any eRASS and in eRASS:4 (if available). Lower panel: Fraction of background sources f_bkg expected to be detected in eRASS1 from a simulation by Seppi et al. (2022).