Bayes Rule appears occasionally on MathCounts, and it helps to have clear notation. In this case M represents passing his math test and –M represents not passing math. Same for S and –S for passing and not passing the science test. P(M|–S) means the probability she passes math given she did not pass science.
I write out all the known data at the top, then use the formula for Bayes Rule to work through the computations. Finally, I take one more look at what the questions is asking and add together the appropriate probabilities.