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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