# Conditional Probability

Conditional probability refers to the case where we have some data that could modify the probability that a certain event has occurred.

Example from everyday life:

If we are asked what is the probability that the first girl to leave the classroom has brown hair.
We won't know how to say.
But, if we are provided with information that in the classroom there are only $2$ blonde girls among $30$ girls in total, the probability we can present will be different.

Let's look at a more advanced example:
In the fifth grade of the Normal School, there are boys and girls.
$13$ girls.
$12$ boys.
Some students participate in the music class and others do not.
$5$ students participate in the music class.
$20$ students do not participate in the music class.

More data:
$3$ boys from the grade participate in the music class.
$7$ girls from the grade participate in the music class.

Let's organize the data in a table:

 Total They do not participate in the music class Participate in the music class You haven't provided any content for translation. Could you please provide the text or HTML content you need translated from Spanish to English? 12 Yes Here it will be 9 I'm sorry, but it seems like there was a mistake in your request. You've only provided a number "3" without any context or content to translate. Could you please provide the text or HTML content you need translated from Spanish to English? Children 13 Yes Here it will be 6 7 Girls 25 20 5 Total

The key to successfully solving conditional probability exercises is to identify the given data.
What we know will appear in the denominator.
What we don't know will be in the numerator and will represent a certain part within the data we already have.
Now, if we were asked about the probability of randomly selecting a student from the grade and getting one who participates in the music class, we could look at the table and see that
$7$ girls out of the $13$ in the grade participate in the music class, therefore, the probability will be:
$\frac{7}{13}=0.538$

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

Probability for 14-year-old students

Probability of independent random events

Dependent random events

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

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