If you draw two cards, what is the probability that the second card is a queen? We had this question arise in class today and I still don't understand the answer given. We were to assume that drawing cards are independent events. We were asked what the probability that the second card drawn is a queen if we take two from the deck. The answer given was 4/52, which seems counter-intuitive to me. How is the probability still 4/52 if there was a card drawn before it? What if the first card drawn was a queen?
There are two cases here:

Case 1: First card chosen is a queen

$$\frac{4}{52}*\frac{3}{51}=\frac{1}{221}$$

Case 2: First card chosen is not a queen.

$$\frac{48}{52}*\frac{4}{51}=\frac{16}{221}$$

Adding both the cases, we get $\frac{17}{221}$ = $\frac{4}{52}$ = $\frac{1}{13}$
I would think it would be slightly below 1/13 since 1/13 is the probability for the first pick being a queen then the second round should account for the possibility of there only being 3 queens in the deck.