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?
Probability – Probability of Drawing a Queen as the Second Card
probability
Best Answer
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 $\frac{17}{221}$ = $\frac{4}{52}$ = $\frac{1}{13}$