Probability Theory Basics

## Multinomial Distribution

The multinomial scheme extends the Bernoulli trial in cases with more than two outcomes. A multinomial scheme refers to a situation where you have multiple categories or outcomes and are interested in studying the probabilities of each outcome occurring. A probability distribution that models the number of successes in a fixed number of independent trials with multiple categories is called multinomial distribution.

Let's look at the example:
A company is surveying to gather feedback from its customers.
The survey has three possible responses: "Satisfied," "Neutral," and "Dissatisfied." The company randomly selects `50` customers and records their responses.
Assume that each customer is satisfied with a probability `0.3`, neutral with a probability `0.4`, and dissatisfied with a probability `0.3`.
Calculate the probability that there will be `25` "Satisfied" responses, `15` "Neutral," and `10` "Dissatisfied".

To solve this task multinomial distribution is used:

In the code above, we used `.pmf()` method of `scipy.stats.multinomial` class with parameters `n` (number of trials) and `p` (probabilities of each outcome) to calculate probability that we will have certain `response` (the first argument of the `.pmf()` method.