posted by Lorrie .
Event A represents the act of drawing a rank of eight from a standard deck of 52 cards, if B represents the event of drawing any diamond after the first card has been replaced into the deck, what is the probability of A and B.
By "rank of eight" I assume you mean any eight card. The probability of that happening on the first draw is 4/52.
Since tha first card drawn is then replaced in the deck, the probability of drawing a diamond in the next draw is 13/52, and you just multiply the two probabilities.
The answer would therefore be (4/52)*(13/52) = 1/52.