stands for B complement.
Then exactly one is:
.
You finish!
Suppose A and B are events and define the new event C to occur if and only if exactly ONE of A or B occur. Show algebraically, using only the probability axioms and properties, and basic set-theoretic results , that
P(C) = P(A) + P(B) - 2P(A n B)
(n is meant to be an intersection symbol