**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 $⅕$ ).

**If you are interested in this article you may also be interested in the following articles:**

- Statistics
- Data collection and organization - statistical research
- Statistical Frequency
- Relative Frequency in Statistics
- Key Metrics in Statistics
- Possible outcomes and their probability
- Representing probability on the number line
- Frequency probability
- Relative frequency in probability
- Properties of probability

**In** **Tutorela's****blog**** you will find a wide variety of mathematical articles**.