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)$.


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

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

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

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

So did I get it right?


Yes, it's right. You can draw a Venn's diagram to see it


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