A number n of particles are instantly released in a semi-enclosed basin at a 
given point and subsequently dispersed by water motions. The dispersion 
processes considered here imply that all the particles eventually leave the 
basin. It is assumed that there is no interaction between the partcles, and that 
the probability c(t) of finding a particle in the basin at time t is the same 
for all the particles. Thus, the histories of the particles are independent 
realizations of the same process. Let N(t) be the random variable "number of 
particles in the basin at time t". It follows that the probability distribution 
of the events N(t)=i, 1=0,1,...,n, is a binomial distribution. The basic 
properties of the stochastic process N(t) are illustrated: time dependence of 
the probability distribution, and of its numerical characteristics mean value 
and variance; when the binomial distribution can be approximated by the Poisson 
distribution; the probability distribution of the events "at least (most) i 
particles are in the basin at time t". Numerical experiments have been performed 
by applying Lagrangian models to various sample problems, confirming the results 
of the theoretical analysis.