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

Law of Total Probability

It is time to gain insight into theoretical terms! Let's start.

The first crucial term is exhaustive events.

What is it?

This term describes when at least one event must happen.

Example:

The simplest and the most evident example is tossing a coin. The probability of receiving head or tail is 50%, but together they result in 100%(all outcomes). In other words, the events are exclusive.

Moving on, let us look at another term i.e. law of total probability.

To understand better, it is better to solve one task.

Example:

Imagine that we have three boxes. The first one contains 7 red balls, the second one contains 5 green balls and the third one contains 4 green balls and 3 red balls. Calculate the probability that we will randomly pull out red ball.

So, the result is 0.47619048, to find it we should multiply the probability to pick a specific box by the probability to pull out the box from this column.

Everything was clear?

Thanks for your feedback!

Section 2. Chapter 6

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