Question

How do you know when to use a poisson distribution or binomial distribution?

Answer 1

Hint: We first discuss the types of distribution by using common terms. Then we express the individual events where we can use the particular distribution. There is no “set of rules” for knowing when to use which equation. Judgment should be used when reading over a question to try to distinguish which probability function to use.

Complete step by step solution:
We first discuss the two types of distributions and the particular cases where using them is most appropriate.
Binomial distribution describes the distribution of binary data from a finite sample. Thus, it gives the probability of getting r events out of n trials.
Poisson distribution describes the distribution of binary data from an infinite sample. Thus, it gives the probability of getting r events in a population.
If a mean or average probability of an event happening per unit time etc., is given, and we 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 we are asked to calculate the probability of this event happening k times out of n, then the Binomial Distribution must be used.

Note:
Once all the data is organized, we need to understand what the question is asking for. This step is important because sometimes a question can give unnecessary data, and we must determine what values to use.