Question

Let A and B be events in a sample space S. Prove that A and B are independent

if and only if P(A | B) = P(Ac

| B).

Answer 1

From the Venn diagram, we see that the events A ∩ B and A ∩ B' are mutually exclusive and together they form the event A. Using this argument and the definition of a conditional probability one finally concludes events A and B are independent.