Course Content

Probability Theory

Have you ever wondered how often you usually use the word probability? It is time to dive deeper into this very familiar term!

Please take a look at the simplest example: imagine that you toss a coin, it is always a

50%chance of gettingheadortail. I mean that there are onlytwo possible outcomes, and the probability for each case is1/2(1/2 equal to 50 %).

It is time to turn to the definition of the **random variable** and clarify how we received such numbers.

The **random variable** is a quantity that equals one and only one value depending on the result of testing result.

Let's assume that **X** is the **random variable** with several outcomes (getting head or tail); therefore, we can mark them as **x1** and **x2**.

The formula for **calculating the probability** is the following:

Let's build a small table for the probability distribution of random variables:

I hope you're interested in learning probability theory now! Here, it would be best to memorize the formula written above and the definition of a random variable.

Indeed, each event can result either in success or failure. For instance, if you have a box with balls colored differently (red or green) and want to put a red one, your event has two outcomes: red ball or not a red ball.

The picture for the task:

Section 1.

Chapter 1