Two kings in a row — Probability Aptitude Question
Two kings in a row: Two cards are drawn without replacement from a pack of 52. What is the probability that both… Answer and worked solution on CodeKairo.
- Topic: Probability
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
Two cards are drawn without replacement from a pack of 52. What is the probability that both are kings?
Options
- 1/169
- 1/221
- 1/13
- 4/663
Show the answer and the worked solution
Correct answer: B. 1/221
Worked solution
- P(first king) = 4/52 = 1/13.
- P(second king given the first) = 3/51 = 1/17.
- Product = 1/221.
Answer: 1/221.
The idea
Without replacement, reduce both the favourable count and the total after each draw. With replacement it would be (1/13)² = 1/169, which is offered.
Shortcut. Count pairs: C(4,2) = 6 king pairs out of C(52,2) = 1,326 pairs, and 1,326 ÷ 6 = 221, so 1/221.
Common trap. "1/169" — using 4/52 for both draws, as if the first king were put back; without replacement the second draw is 3/51.