Disclaimer: This is homework, however I am not looking for an answer. I'm only trying to understand the actual question.
I'm given four mutually exclusive and exhaustive events: $A$, $B$, $C$, and $D$. I'm also given $P(A)$, $P(B)$, $P(C)$ and $P(D)$. There is also some minor event $M$, for which I have $P(M|A)$, $P(M|B)$, $P(M|C)$ and $P(M|D)$.
Now for the actual question:
Given that a problem is due to the problem $M$, what is the probability that $B$ occurs?
What exactly is this saying? Would it be proper to say that is it asking for:
$ P(B|M) $
Which could be solved using:
$ \frac{P(B)}{P(M)} $
Seeing as they are mutually exclusive?