Let us assume that the clusters in the sky have the same size,

, a Poissonian distribution, and the same number of galaxies up to a given magnitude,

(galaxies/cluster). This is a very rough model, because it is clear that

and

depend on the redshift; however, for our present arguments, the estimation with mean values of

and

is enough. In such a case, the total number of galaxies, N, is:

(14)

where

is the density of field galaxies (galaxies/deg

^{2}) and

is the density of clusters (clusters/deg

^{2}). An example of a probability calculation would be the one to have three galaxies belonging to three different clusters in the area A (we assume that they have the same magnitude, for a simplistic calculation, although it can be generalized to any magnitude distribution), i.e. the probability of three clusters being in the line of sight multiplied by the probability of three galaxies from different clusters being in the area A of the filament given the density of galaxies in a cluster,

(15)

that is, the probability is lower than

, which is the probability we calculated in (8). Therefore, the supposition of a line of sight with three clusters would make the probability smaller instead of larger, and similarly for a lower number of clusters.