Note that in this question there are four probabilities to consider. P(A), P(B), P(A intersection B) and P(A union B).
the chance for it to occur should be A/A+B and if we take the probability of that this should be P(A)/P(A union B)
P(A union B)=P(A)+P(B)-P(A intersection B) [Use a venn diagram if unsure]
in mutually excluse P(A intersection B)=0
therefore the chance for A to occur first is P(A)/[P(A)+P(B)]
The key here is P(A intersection B)=0. Whenever you deal with mutually excluse just remember that and try to put that somewhere.