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It is straightforward to show the probability of an eclipse at any depth is $P_e = r_s + r_g$ but the authors wish to study the probability of an eclipse of \textbf{any specified} magnitude depth.  \paragraph{}  In order to calculate this probability, the function $i(\Delta m)$ must be derived. Although the maximum primary eclipse depth $\Delta m$ is a well defined function of the inclination angle i, iteration is needed to find this inverse function $i(\Delta m)$  \paragraph{}  With a random distribution of inclinations the probability of a primary eclipse deeper than $\Delta m$ is $cos(i(\Delta m))$  \paragraph{}    The mean values for eclipse probabilities are meaningful only for similar sized systems (radii, luminosities and orbit sizes) so the authors have divided the HR diagram into a number of bins, and each bin is further subdivided according to orbital period and $\Delta m$. The final results are thus histograms giving the mean probability $P_e(\Delta m, P)$ for each HR bin.  \paragraph{}  The authors have also included another type of probability which is useful when comparing the synthetic population with observations: namely the fraction of eclipsing binaries relative to all stars (single and binary) in the same HR diagram bin. The authors derive this 'normalized probability' $O_e(\Delta m, P)$