We can use the above decomposition to do that, however I think it is easier to do this other way.
We will use the formula, valid for any events A,B:
Proofs scare the living daylights out of me! I could really use some help with this:
For some experiment, suppose B and C are events. The event, D, that "exactly one of the events B and C occur" is of interest.
(a) Show that D can be written as a union of disjoint events.
(b) Show that P(D) = P(B) + P(C) -2P(B intersect C).