Over the past years, 90% of Stats students study for the first midterm. Of those who study, 30% get an A grade on the first midterm, whereas 5% of those who do not study get an A grade. If you learn that a randomly selected student has an A grade on the first midterm, what is the probability that he/she studied?
OK so with this data, then: $$ \Pr(S) = 0.9 \\ \Pr(A|S) = 0.3 \\ \Pr(A|S') = 0.05 \\ $$
Where $\Pr(S)$ is the probability of studying and $\Pr(A)$ is the probability of getting an A.
I think I am looking for $\Pr(S|A)$. The formula I know for this is:
$$ \Pr(S|A) = \frac{\Pr(A∩S)}{\Pr(A)} $$
The issue is that I don't know either of those probabilities. I am not sure where to go from here.