The everyday definition of the term "probability" is the chance that a particular event will occur.

For example:

What is the probability that when we roll a die we will get the number. $2$?

What is the probability that when tossing a coin we get "heads"?

So, as can be understood, probability is the numerical expression for the occurrence of a particular event:

Consider the following example:

When tossing a die, the possible outcomes are any of the numbers between. $1$ and $6$.

Any outcome between $1$ and $6$ is a possible event.

The outcome $7$, for example, is not possible, so $7$ is an impossible event.

The probability is calculated as follows:

If we go back to our previous example and throw the dice, what is the probability that we will get the result $2$?

• The number of possibilities of the searched case $1$ (because there is only one outcome that is possible for us)
• Total options: $6$ (the total possible outcomes are from $1$ to $6$)

Therefore, the probability of rolling a die to get the outcome $2$ is $⅙$.

And now let us consider what is our probability of obtaining an outcome between $1$ and $3$ on a single roll of the dice?

• The number of possibilities of the searched case $3$ (each of the outcomes $1,2,3$ meets our requirement)
• Total options: $6$ (the total possible outcomes are from $1$ to $6$)

Therefore, the chance of rolling a single die to get an outcome between $1$ and $3$ is $\frac{3}{6}$, each of them is a "possible event".

In the same way, we can check what is the probability that we get the result $7$?

• The number of possibilities of the requested case $0$.

Therefore, the chance of rolling our die to get the result $7$ is $0$; this is an "impossible event".

What is the probability that we get a result between $1$ and $6$?

• The number of possibilities of the requested case $6$ ($1,2,3,4,5,6$ All possible outcomes in fact)
• Total options: $6$ (total possible outcomes are from $1$ to $6$)

Therefore, the probability of dropping a single die to obtain an outcome between $1$ and $6$ is $6/6$, i.e. $1$. This outcome is a "certain event".
As can be seen, the probability will always be between $0$ and $1$, where probability 0 is an impossible event, probability $1$ is a certain event and everything in between is a possible event.

We will look at probability on the numerical axis:

Probability allows us to calculate different possibilities and situations. For example:

• Frequency: the number of times we obtain a certain outcome.
• Common: the result obtained more times
• Relative frequency: the number of times a certain result was obtained out of the total number of results:

For example:

We rolled the dice ten times and obtained the following results:

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

What is the frequency of the result $3$?

We obtained the result $3$ twice so the frequency is $2$.

What is the common result in our experiment?

$5$ is the result obtained the most number of times and therefore the most common is $5$.

What is the relative frequency of the result $3$?

We obtained the outcome $3$ twice out of the ten times we rolled the die. Thus, the relative frequency of the outcome $3$ is $\frac{2}{10}$ (or $⅕$ ).

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