Prove $P(B|A) = P(B)$, if $A$ and $B$ are independent

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How can I show that $P(B|A) = P(B)$, given that $A$ and $B$ are independent?

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Llease use the definitions of independent events and formula of conditional probability

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Welcome to MSE:)

Recall the definition for independence RV. first $$p(A,B)=p(A)p(B)$$

Then recall the equation for conditional probability $$p(A,B)=p(B|A)p(A)$$

Taking them together, Voila, you get what you want right?