independent events in statistics

[stevecallaway]

1. The problem statement, all variables and given/known data
Two cards are drawn from a standard deck with replacement. A=first card is an ace. B=second card is an ace. Show that A and B are independent


2. Relevant equations
P(A and B)=P(A given B)/P(B)
P(A given B)=P(A)

3. The attempt at a solution
P(A)=4/52
P(B) =4/52
P(A and B)=[(4/52)(4/52)]/(4/52)=(4/52)=P(A)
So the question I'm having is how to find P(A and B)?
Am I correct that P(A and B)=(4/52)(4/52)?

[LCKurtz]

Is your definition of independence that P(B|A) = P(B)? You have already calculated P(B) = 4/52 = 1/13.

Now, given that A has happened, and the card has been replaced, what is P(B) then? That would give you P(B|A). If it is the same as P(B), you are done.