Sheldon Ross describes the following as examples of random variables that generally obey the Poisson probability law:
$1.$ The number of customers entering a post office on a given day.
$2.$ The number of vacancies occurring during a year in the federal judicial system.
I am aware that the Poisson random variable may be used as an approximation for a binomial random variable with parameters $(n,p)$ when $n$ is large and $p$ is small enough so that $np$ is of moderate size, but how do I think about the two situations above using this piece of information? I am not too sure of what I'd consider independent trials and what I'd consider a success in these case.