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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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"

ANSWER

(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! 🙂

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.

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

-brett

btw, nice blogI’m considering buying the book

Merci! 🙂

-brett