## Interview Question

Quantitative Analyst Interview

-New York, NY

Jane Street## You have 2 decks of cards (each deck contains both red and black cards). One deck has twice the number of cards in the other deck with the same color ration (so one deck has 52 cards and the other has 104, both half red and half black). I offer you to play a game. First you get to chose which deck of cards you want to play with. Second, you draw 2 cards at random from your deck of choice. If both are red, then I will give you a ferarri. Which deck of cards would you chose?

Answer

## Interview Answers

13 Answers

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17

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The unalert interviewee would answer "it doesn't matter, the probability is the same". While this is true for the first card, you have a higher probability of drawing a second red card with the big deck than the smaller one. So I chose the big deck (no homo) and I was right.

Anonymous on

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extreme case deck 1: 1 red 1 black deck 2: 2 red 2 black So more cards the better chance you get...

xc on

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Mathematically: (26/52 * 25/51) vs (52/104 * 51/103) 51/206 > 25/102

G on

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"G" did the right calculation. To calculate the probability of drawing two red cards in a row one needs to set up an equation where the first drawn was red, and the SECOND card was red as well. The question is asking what is the probability of drawing 2 red cards in a row, NOT what is the probability of drawing a red card then either a red or black card.

"No" is wrong on

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Intuition tells us if you add in same number of red and black cards into the original problem with 52 cards, probability will go up. Just imagine when you add in 1 billion red cards and 1billion black cards

Anonymous on

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You should definitely choose the larger deck if both are 50% red, 50% blue. Here's another explanation in addition to the other correct ones above. Each deck is naturally partitioned into maximal sub-stacks where each sub-stack consists of cards of a single color, either all red or all blue. If it is known ahead of time that half the cards are blue and half are red, then the expected size of the stack increases with the number of cards in the deck.

nilkn on

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Correction: expected size of the **sub-stacks** increases with the number of cards in the deck. Sorry about that.

nilkn on

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Either one.

Chris Medina on

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If you don't like how the table is set, re arrange it. I would offer the dealer half of the reward if he/she let me draw 5 more times in the deck with more cards.

(╯°□°)╯︵ ┻━┻ on

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It seems that the odds are greater with a lager number of choices. 2:1 ratio.

The larger deck on

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2 out of 52 is the equivalent of 4 out of 104. For these chances to be equal then the problem should be 2 out of 52 or 4 out of 104. If you still get to draw only two cards to try to get two reds then the chances should be better with the smaller deck.

cisprof on

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yes, he would be right

prm on

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Actually, the probabilities are the same for each deck. Consider than because you have a 50/50 chance of drawing your first card red, there's a 50% chance the numerator of the next fraction is reduced by one..so your probability is 26/52 * (25/51+26/51)/2 vs 52/104 * (51/103+52/103)/2 which are the same

No on

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