Course Content

Probability Theory Basics

1. Basic Concepts of Probability Theory

Stochastic Experiment and Random Event Probability and It's Properties Geometrical Probability Challenge: Solving the Task Using Geometric Probability Independence and Incompatibility of Random Events Conditional Probability

2. Probability of Complex Events

Inclusion-Exclusion Principle Challenge: Solving the Task Using Inclusion-Exclusion Principle The Multiplication Rule of Probability Law of Total Probability Bayes' Theorem Challenge: Solving the Task Using Bayes' Theorem

3. Commonly Used Discrete Distributions

Binomial Distribution Challenge: Solving Task Using Binomial Distribution Multinomial Distribution Geometric Distribution Poisson Distribution Challenge: Solving Task Using Poisson Distribution

4. Commonly Used Continuous Distributions

Continuous Uniform Distribution Exponential Distribution Challenge: Solving Task Using Exponential Distribution Gaussian Distribution Challenge: Solving Task Using Gaussian Distribution

5. Covariance and Correlation

What is Covariance?What is Correlation?Challenge: Solving the Task Using Correlation

Challenge: Solving the Task Using Geometric Probability

Consider a square with a side length of 2 units centered at the origin (0, 0) in a Cartesian coordinate system.
What is the probability that a randomly chosen point within the square doesn't fall into a circle with a radius of 1 unit centered at the origin?
As we have a two-dimensional space of elementary events, we can calculate the ratio of the circle's area to the square's area. The ratio represents the probability of a point falling within the circle.

Task

Calculate probability as the ratio between the blue area and the whole area of the square.

_{Once you've completed this task, click the button below the code to check your solution.}

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Section 1. Chapter 4

Challenge: Solving the Task Using Geometric Probability

Task

Calculate probability as the ratio between the blue area and the whole area of the square.

_{Once you've completed this task, click the button below the code to check your solution.}

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Section 1. Chapter 4

Challenge: Solving the Task Using Geometric Probability

Task

Calculate probability as the ratio between the blue area and the whole area of the square.

_{Once you've completed this task, click the button below the code to check your solution.}

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Everything was clear?

Thanks for your feedback!

Task

Calculate probability as the ratio between the blue area and the whole area of the square.

_{Once you've completed this task, click the button below the code to check your solution.}

Switch to desktop for real-world practiceContinue from where you are using one of the options below

Section 1. Chapter 4

Switch to desktop for real-world practiceContinue from where you are using one of the options below