# Probability of Independent Random Events

## What are independent random events?

Independent random events are those that occur independently of each other. No event influences the probability of another event occurring or not.

## Let's see it in the formula:

$P(A\cap B)=P(A)\times P(B)$

Apart from calculating the probability of independent random events with the formula, we can also do it in other ways.

## Double-entry table to find the solution to probability questions

The double-entry table will show the parameters clearly so that we can quickly calculate the required probability.

Let's continue with the second method:

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## Probability calculation with area in a double-entry table

The calculation of the square's area will indicate the probability of both the event indicated in the length and the one indicated in the width occurring.
As the formula for the calculation says, we will multiply the length by the width and obtain the sought probability.

Let's continue with the third method:

## Probability Calculation with Dendrogram (Tree Diagram)

The dendrogram describes the procedure carried out in the trial.
To find the probability that describes what has occurred in the first event and also what has occurred in the second, we will multiply the corresponding probabilities represented on the branches.

## Example from daily life about the probability of independent random events

First event: The barber wore a green shirt
Second event: Today I prepared an egg sandwich
The symbol for independent random events is$∩$
If we want to indicate that the events are $A$ and $B$ independent random events, we will do it as follows:
$A∩B$
We will denote probability with the letter $P$
The probability of independent random events will be equal to the product of the probabilities of the two events separately.
That is, probability of event $A$ times probability of event $B$ .

### Double-entry table to find the solution to probability questions

The double-entry table will show the parameters clearly so that we can quickly calculate the required probability.

In the table there will be two columns and two rows.
First column
will indicate the probability that the first event has occurred.
Second column
will indicate the probability that the first event has not occurred.
First row
will indicate the probability that the second event has occurred.
Second row
will indicate the probability that the second event has not occurred.
Inside the table, the probabilities of both events will be shown respectively.
Note: The probability that a certain event occurs, added to the probability that a certain event does not occur will always be$1$.

### Probability calculation with area in a double-entry table

This table will be composed in a way similar to the double-entry table.
We will note next to each length and width the corresponding probability.
The calculation of the area of the square concerning will indicate the probability of both the event indicated in the length and the one indicated in the width occurring.
As indicated by the formula of the calculation, we will multiply the length by the width and obtain the sought probability.

### Probability Calculation with Dendrogram (Tree Diagram)

The dendrogram describes the process carried out in the experiment.
Let's draw two branches that describe the probability of the first event occurring and the probability of the first event not occurring.
From the branches we have drawn, let's draw another pair of branches from each, describing the probability of the second event occurring and the probability of the second event not occurring.
To find the probability that shows what has occurred in the first event and also what has occurred in the second, we will multiply the corresponding probabilities represented on the branches.

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

Probability for 14-year-old students

Dependent random events

Conditional probability

In the Tutorela blog, you will find a variety of articles about mathematics.

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