Probability | Tutorela

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 $⅕$ ).