How do you know when to use a Poisson distribution or binomial distribution?
As a short guide
If a mean or average probability of an event happening per unit time etc., is given, and you are asked to calculate a probability of n events happening in a given time etc then the Poisson Distribution is used.
If, on the other hand, an exact probability of an event happening is given and you are asked to calculate the probability of this event happening k times out of n, then the Binomial Distribution must be used.
The Poisson distribution can be derived as a limit of the binomial distribution.