Difference between Poisson and Binomial distributions.?

Question

If both the Poisson and Binomial distribution are discrete, then why do we need two different distributions?

Answer 1

They model different things

Binomial Distribution occurs when the probability of a "success" is known (to be 0 < p < 1)

and the goal is to find the probability of k successes in N-trials 0 < k < N , all integers.

Poisson is used to model randomly occuring phenomena

Ex. frequency of customers entering a place of business...

frequency of telephone ringing at the help desk...

frequency of getting bite when fishing... etc.

To do this type of model, there must be at least an average, of how many times the event

occurs in a given time frame