Probability Theory

Probability Theory

0%

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

Multiply probabilities

Sometimes it is impossible to pick one event, hence, we should refer to the multiplication rule for independent events.

Independent events mean that the occurrence of one event doesn't depend on another event like flipping two coins or rolling two dies.

Let's talk about the multiplication rule.

Where can I use it?

In a situation where we certainly know that we are interested in more than one event.

Example:

Imagine rolling two dice; calculate the probability that the multiplication of numbers on the edge of two dice is 36. The first one has 6 on its dice and the second one has 6 on its dice.

Explanation:

Here is the formula:

Explanation:

If we want to receive success for both the first and second events, we should multiply the probability of getting a win in the first event and the second. The key for the multiplication rule is and. If you see the phrase the first and the second event you should use the multiplication rule.

Everything was clear?

Thanks for your feedback!

Section 2. Chapter 4

some-alt