Another confusing stats question

• January 30th 2009, 08:20 AM
mitch_nufc
Another confusing stats question
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
• January 30th 2009, 08:51 AM
Plato
$\overline B$ stands for B complement.
Then exactly one is:
$P\left( {A \cap \overline B } \right) + P\left( {\overline A \cap B} \right) = P(A) - P(A \cap B) + P(B) - P(A \cap B)$.
You finish!