Problem of fractions and percents I don't know how to approach.

Question

I have a long cuestionary with this type of question but I hadn't found the way to solve this. I will appreciate any advice you can give me.

In a certain school, $\frac{3}{4}$ of the students who like to practice soccer also like to practice volleyball. $\frac{3}{4}$ of the students who like to practice volleyball also like to practice soccer. Additionally, $\frac{3}{4}$ of the students don't like soccer or volleyball. What is, in this school, the percent of students who like practicing both sports?

Answer 1

You have learned some basic rules about probability. You are given

1. $ P(V|S) = 3/4$.
2. $ P(S|V) = 3/4$.
3. $1-P(S \cup V) = 3/4$.

You can express $ P(S) $ using $ P(S \cap V) $ from (1) and $ P(V) $ from (2) using one of the rules you learned. Now using (3) and one of the basic rules you can find $ P(S \cap V) $.