We know that the probability of occurrence of A given that B has already occurred is given by,
P(A|B) = P(A&B) / P(B)
We know that A and B are independent events if P(A & B) = P(A) P(B)
Substituting this in the equation we get,
P(A|B) = P(A) P(B) / P(B)
P(A|B) = P(A)
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