Probability Theory

Probability Theory

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1. Learn Basic Rules

It's time to dive deeper into the probability theory. Here we will learn basic formulas. The main idea of the section is to help to understand the term probability using real-life examples.

Random Variable

Bernoulli Trial 1/2

Bernoulli Trial 2/2

Binomial Probability 1/2

Binomial probability 2/2

2. Probabilities of Several Events

Here, we will get acquainted with the rules in probability theory. This section will be more complicated than the previous one. It will be attractive because we are going to work with the real challenges. But it should be noted that we learn some formulas.

Add Probabilities

Calculate Connected Probabilities

Multiply probabilities

Dependent probabilities

Law of Total Probability

3. Conducting Fascinating Experiments

Doing experiments is always funny, but here we will combine exciting tasks with programming learning. In this section, we will work with the binom object to conduct experiments in Python.

The First Experiment

The Second Experiment

The Third Experiment

Combine Your Knowledge

4. Discrete Distributions

Distribution is a key to probability learning, but don't be petrified by this term. This section provides you with real-life explanations and relevant formulas.

Discrete Uniform Distribution

Calculate Fascinating Probability

Bernoulli Distribution

Binomial Distribution

Poisson Distribution

5. Normal Distribution

The normal distribution is the most commonly used one. Here we will work with the distribution with the help of real-life challenges.

Normal Distribution

Course Content

Probability Theory

Probability Theory

1. Learn Basic Rules

Random Variable Bernoulli Trial 1/2 Bernoulli Trial 2/2 Binomial Probability 1/2 Binomial probability 2/2

2. Probabilities of Several Events

Add Probabilities Calculate Connected Probabilities Challenge Multiply probabilities Dependent probabilities Law of Total Probability Bayes Theorem Challenge

3. Conducting Fascinating Experiments

The First Experiment The Second Experiment The Third Experiment Combine Your Knowledge

4. Discrete Distributions

Discrete Uniform Distribution Calculate Fascinating Probability Bernoulli Distribution Binomial Distribution Challenge Poisson Distribution Challenge

5. Normal Distribution

Normal Distribution Challenge 1 Сhallenge 2

Add Probabilities

Probability theory can describe a many situations in our lives; for that reason, learning it should be interesting!

It's time to talk about the addition rule.

Where can I use it?

In situations when either one of the events should happen. Events should be absolutely independent.

Example:

At the beginning of the course, we acquinted ourselves with the definition of probability theory with the example of balls. But now, this example will be complicated.

Calculate the probability of getting either a green or blue ball if you have 9 blue balls, 13 red balls, and 7 green balls.

Explanation:

So, to calculate the probability of success for the events connected by the word or (get the blue or green ball from the box), we should calculate the probability for the first event, then add the probability for the second event, and so on. We can use this schema for calculating three, four, or even a million possibilities, and just calculate the probability for each of them, and finally add.

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Section 2. Chapter 1

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