Two cards are drawn one after the other, without replacement, from a well-shuffled pack of 52 playing cards. If the first card drawn is a king, then the probability that the second card is also a king is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{1}{17}\)
After one king is drawn and not replaced, the pack has 51 cards, of which 3 are kings.
\( \displaystyle P(\text{second king} \mid \text{first king}) = \frac{3}{51} \)
\( \displaystyle = \frac{1}{17} \)
Why the other options are incorrect
Option (1) \(\displaystyle\frac{1}{13}\) — Incorrect. This is \(\frac{4}{52}\), the answer if the first card were put back.
Option (3) \(\displaystyle\frac{1}{221}\) — Incorrect. This is \(\frac{4}{52} \times \frac{3}{51}\), the probability that both cards are kings, which ignores that the first king is already given.
Option (4) \(\displaystyle\frac{4}{51}\) — Incorrect. This still counts 4 kings, but one king has already been taken out.