## Interview Question: A Card Question

Sample Question #126 (probability theory)

A deck of playing cards is shuffled thoroughly and placed face down. You take the top two cards, faced down, from the deck. You flip over the first card you drew and it’s a King. What’s the probability that the second card you drew is also a King?

(Comment: card-inspired probability questions are very popular at quant interviews)
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### 6 Responses to Interview Question: A Card Question

1. Unknown says:

Wouldn’t the answer be simply three divided by the number of remaining cards?It would be different if the question was something like "at least one of the two cards is a king"

2. Brett says:

(corrected)

Before you answer the question, you should first ask the interviewer whether the deck contains the Joker, and, if so, one or two Jokers. Asking for the clarification is important for two reasons: one, it affects the calculation; two, it shows you’re detail-oriented.

Then, as French visitor "no name" points out, after the first card is revealed to be a King, there’re just three Kings left so the probability of the second card on top being King is — assuming no Jokers in the deck — just 3/51.

You can verify this by calculating the conditional probability:

Pr(2nd card is also King | 1st card on top is King)
= Pr(both 2 cards on top are King) / Pr(1st card on top is King)
= [(4×3) / (52×51)] / [4 / 52]
= 3 / 51

Thanks, "pas de nom," for pointing the obvious solution! 🙂

3. Ming says:

I agree with pas de nom, as I think given the way this question is presented, the conditional part has already been taken out of the equation.

4. Brett says:

Maybe I screwed up on posing the question…  I’ll find a harder card question next time. 🙂

-brett

5. Unknown says:

btw, nice blogI’m considering buying the book

6. Brett says:

Merci!  🙂
-brett