Course Content

# Probability Theory Basics

4. Commonly Used Continuous Distributions

5. Covariance and Correlation

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.

What is the multinomial distribution?

Select the correct answer

Everything was clear?