Event A has A size sample space. Event B has B size sample space.

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.