Events, Probabilities, Classical probability, Desired cases/all cases, Elementary events, Union.
Let's start with a very simple thing. We have a die, roll it once, and see what kind of events could occur.
We may roll a 1.
It's also possible, that we roll a 2.
Then, it is also possible that before the die stops, a meteorite hits Earth and destroys the die, along with the entire human civilization.
Well, in this case the rolling is invalid. At the beginning, we will only look at cases when the roll is valid, that is, when we get one of the six numbers.
This is called classical probability, and that's what we will discuss for a while. Meteorites will come later.
So, we have a total of six cases. These events are called elementary events.
There are events that consist of more than one elementary events. For example, rolling an even number.
Or, rolling a number greater than 2.
We will use uppercase letters to refer to events.
Every event has a probability. We compute that by counting how many elementary events are included in it, and divide that by the total number of elementary events.
Therefore, all probabilities are between 0 and 1.
We can create new events from existing events.
Let's see what their probabilities look like.
Well, it is worth to remember these. Now, let's move onto something more interesting.