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 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 1 and 6 6 .

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

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

The probability is calculated as follows:

A- Probability

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

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

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


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

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

Therefore, the chance of rolling a single die to get an outcome between 1 1 and 3 3 is 36 \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 7 ?

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

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


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

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

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


We will look at probability on the numerical axis:

A1-  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 1,2,2,5,5,5,4,3,6,3

What is the frequency of the result 3 3 ?

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

What is the common result in our experiment?

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

What is the relative frequency of the result 3 3 ?

We obtained the outcome 3 3 twice out of the ten times we rolled the die. Thus, the relative frequency of the outcome 3 3 is 210 \frac{2}{10} (or ).


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