Prove that if A and B are independent events, P(A|B) = P(A). (Note that A and B are independent if and only if P(A & B) = P(A)P(B))

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)