# Probabilities of outcomes and events

What is probability?
Probability is actually the chance of getting a certain result.
Imagine you are doing an experiment and you throw a bucket.
Instead of asking the question: what is the probability that we will get $3$ in the bucket? Replace the word probability with chance and you will get an understandable and familiar sentence: what is the chance that we will get $3$ in the bucket?

Certain outcome - an outcome that must and certainly will happen.
Probability of a given outcome - will always be $1$
Possible outcome - an outcome that may occur in some cases. There is a chance that it will happen, but it is not certain.
Probability of a possible outcome - will always be between $0$ and $1$.
Impossible outcome - an outcome that has no chance of occurring.
Probability of an impossible outcome: it will always be $0$.

## What is probability?

Probability is actually the chance of getting a given result.
Imagine you are doing an experiment and you throw a bucket.
Instead of asking the question: what is the probability that we will get $3$ in the bucket? Replace the word probability with chance and you will get an understandable and familiar sentence: what is the chance that we will get $3$ in the bucket?

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## What does possible results mean?

Once we understand that probability is a possibility for a particular outcome, we can explain the first part of the theorem: the possible outcomes.
We will divide the possible outcomes into three groups:
certain outcome, possible outcome, and impossible outcome.

Certain result: a result that must happen and will certainly happen.
For example:
If we put $2$ red papers in a hat and draw one, it will certainly be red.

Possible outcome:

An outcome that may occur in some cases. There is a possibility of occurrence, but it is not certain.
For example:
If we put a blue note and a red note in a hat, there is a possible outcome that if we draw a note, it may be red.
I mean, it can be red. It is not certain that it is red because there is also a blue note, but there is some chance (in this case half) that it is red.

Impossible outcome: an outcome that has no chance of occurring.
For example, if we put two red papers in a hat and draw one, there is no chance that it will be blue. Unless it is a magic hat, but not in our case.
In any case, we will return to our point.
Now that you understand exactly what the outcomes of the possibilities mean, we will learn how to calculate their probability, the chance of their happening, easily and simply.

Probability of certain outcome: it will always be $1$.
How will you remember this?
Think about the fact that, since it is a certain outcome, it will happen no matter what. Therefore, the chance of it happening is $100%$! That is, the probability will be $1$.

Probability of a possible outcome: it will always be between $0$ and $1$.
How will you remember this?
Think of it as an outcome that is likely to happen. The probability is neither zero nor $100%$, so it is somewhere in between, i.e., the probability is greater than $0$ but less than $1$.

Probability of an impossible outcome: it will always be $0$.
How will you remember this?
This is an outcome that will never happen! Its chance of happening is zero, so the probability is $0$.

## Examples and exercises of possible outcomes

We will perform an experiment of throwing a die:

### Example

Imagine a completely normal die with the following numbers:
$1,2,3,4,5,6$

Each number appears on one side, as in a completely normal cube.
Now, we will roll the die and talk about the possible outcomes and their probabilities.

As mentioned, there are $6$ possible outcomes.

We will ask the following questions:

Example to calculate the probability of a certain outcome.

What is the probability of getting a number less than $7$?

All possible outcomes are less than $7$, so getting a number less than $7$ is a certain outcome.
As we have learned, the probability of a certain outcome is $1$. There is a $100%$ that we will get an outcome less than $7$.

Examples for calculating probability of a possible outcome:

What is the probability of getting a number greater than $4$?

To answer this question, we will first examine how many possible outcomes an event has: getting a number greater than $4$.
The answer is only $2$ options. Only the numbers $5$ and $6$ are greater than $4$.
$1,2,3,4,5,6$

Note that the probability is not $2$.
To find the probability, we will have to divide by $2$: the number of possible outcomes for the event we tested divided by the number of all possible outcomes without conditions.

This is $2/6$.

To remind yourself that all possible outcomes must be divided, say to yourself:
For an event that gets a number greater than $4$, there are $2$ of $6$ possible outcomes.
The reminder word will be the fraction line.

Another way to remember:
As you can see, we mark the outcomes that describe the case in red.
We can say to ourselves, we marked $2$ numbers in red out of 6 numbers in total and therefore the probability is $2/6$.

## Additional examples for calculating the probability of a possible outcome

What is the probability of obtaining the number $2$?

$1,2,3,4,5,6$

The die is normal: the number $2$ appears only once on the die.
Therefore, let's say that the probability of getting the number $2$ is $1$ out of $6$ possible outcomes. That is $1/6$.

Another way to tell ourselves:

Mark one outcome in red out of $6$ possible outcomes in total so that the probability of this outcome is $1/6$.

Pay attention: the verbal answer, using the word inside, is just to explain and in the test you will have to present the probability of the number.

How will you be able to check that you are on the right track?

Remember that the probability of a possible result is between $0$ and $1$.
Note that the results we obtained in these sections are: $2/6$ and $1/6$ - numbers greater than $0$ and less than $1$.

Example for calculating the probability of an impossible outcome:

What is the probability of getting a number greater than $8$?

The numbers on the die are between $1$ and $6$. That is, they are all less than $8$.
Therefore, there is no chance that we will get a number greater than $8$ and, in other words, the probability of such an outcome is $0$.
Important to know:
Sometimes you may encounter the word event instead of the word outcome.
For example, a possible event or an impossible event.
Do not stress or think of this word as if it were an outcome or an event.

In conclusion.
The probability of possible outcomes is a total additional expression of the theorem: the possibility of obtaining the outcomes you are asked about. Impossible or possible and, without a doubt, calculate your probabilities easily and without any problem.

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