Finding cardinality of a set given cardinalities of other sets

Question

Among the students doing a given course, there are four male students enrolled in the ordinary version of the course, six female students enrolled in the ordinary version of the course, and six male students enrolled in the higher version of the course. How many female students must be enrolled in the higher version of the course if gender and version of the course are to be independent when a student is selected at random?

I'm not sure how to use the "independent when a student is selected at random" part, but I thought of Bayes' rule but that deals with probabilities and it looks like I want to find a cardinality of the set of females in the higher course.

Answer 1

Label the versions as $O$ and $H$, and suppose $x$ new female students are enrolled in version $H$.

Assuming version and gender are independent, we get \begin{align*} &P(M|O)=P(M|H)\\[4pt] \implies\;&\frac{4}{10}=\frac{6}{x+6}\\[4pt] \implies\;&x=9\\[4pt] \end{align*}