Suppose a teacher gives out two tests. 37% of students pass the first, and 25% pass both. What percent of those who passed the first one also passed the second?
Isn't it just 67.5%? I guess you could use Baye's rule, but these are independent events so you'd just get 67.5% again? Is this right?
I don't see why the two events should be independent, unless the class is so poorly taught (or the students are all such poor learners) that they all guess randomly on all the questions (which, for the sake of this hypothesis, we suppose are all true/false or multiple choice).
But it doesn't matter, because there is no probability involved. Neither Bayes' Rule nor independent events come into play. It is just a simple problem of proportions. There are $N$ students (some unknown number) in the class, $x = 0.37N$ of them passed the first test, $y = 0.25N$ passed both tests, and we want to find $y/x$ as a percentage.
Rounded to one digit after the decimal point I would give the answer as $67.6\%$, but it appears you set up the correct ratio to get the answer.