  The often debated issue of `ratios of small numbers of events' is approached
from a probabilistic perspective, making a clear distinction between the
predictive problem (forecasting numbers of events we might count under well
stated assumptions, and therefore of their ratios) and inferential problem
(learning about the relevant parameters of the related probability
distribution, in the light of the observed number of events). The quantities of
interests and their relations are visualized in a graphical model (`Bayesian
network'), very useful to understand how to approach the problem following the
rules of probability theory. In this paper, written with didactic intent, we
discuss in detail the basic ideas, however giving some hints of how real life
complications, like (uncertain) efficiencies and possible background and
systematics, can be included in the analysis, as well as the possibility that
the ratio of rates might depend on some physical quantity. The simple models
considered in this paper allow to obtain, under reasonable assumptions, closed
expressions for the rates and their ratios. Monte Carlo methods are also used,
both to cross check the exact results and to evaluate by sampling the ratios of
counts in the cases in which large number approximation does not hold. In
particular it is shown how to make approximate inferences using a Markov Chain
Monte Carlo using JAGS/rjags. Some examples of R and JAGS code are provided.
