I am currently learning about conditional probability from "The Book of R" by Tilman Davies and I'm having trouble understanding a conditional probability problem. The problem is as follows:
You randomly draw a card, and after replacing it, you draw another. Let A be the event that the card is a club; let B be the event that the card is red. What is Pr(A|B)? That is, what is the probability the second card is a club, given the first one was a red card? Are the two events independent?
This assumes your standard 52 card deck. I understand that Pr(B) = 26/52, however where I get stuck is when the question asks about clubs which are black and not red. This means that it is impossible to pull a club out of the new sample space (now 26) because clubs are black and not red. The answer key to the book says the final value is 13/52 but I have absolutely no idea how that conclusion was reached. I have always struggled with understanding probability so any help anyone could provide I would greatly appreciate.