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
12	Yes Here it will be 9	3	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:
$\frac{7}{13}=0.538$