# Find the probability that A or B occurs but not both.

Question: Let A and B be events on a probability space. Find the probability that A or B occurs but not both. Express your answer in terms of P(A), P(B), and $P(A\cap B)$.

Soln:

$P(A\cap {B^c})+P({A^c}\cap B)$

$=P(A\cup B) - P(B) + P(A\cup B) - P(A)$

$=[P(A)+P(B)-P(A\cap B)-P(B)]+[P(A)+P(B)-P(A\cap B)-P(A)]$

$=P(A)+P(B)-2P(A\cap B)$

So did I get it right?