Jane Street
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Jane Street Intern Interview Question

"If I spin a roulette, roll a dice, and pick a card out of a 52-card deck, what are the chances that all three are the same number? How confident are you in your answer?"
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Assuming Aces to be "1", the probability is (4x6)/(52x6x38) = 1/(13x38) = 1/494. Again, you need to be able to do this kind of stuff in your head, and quickly. Lay out all your assumptions (e.g. aces are "1", or aces are not "1"), and you should ask in cases you are not sure (if you didn't know a roulette as 38 slots).

For part 2, the interviewer may ask you to bet on your answer with him. This is just a test of how confident you are. For example, I initially arrived at the wrong answer because I thought there were 36 slots in a roulette. I did the calculation right with the wrong number, and I said I was 95% confident. He made a bet with me, where he asked me how much I'd be willing to bet, if he gave me $1 if I were right. Needless to say I lost $19 :(
- Interview Candidate on Feb 11, 2011 Flag Response
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Could someone clarify where the (4x6) in the numerator comes from? I would have thought it would be (4/52)(1/6)(1/38) = 1/13*6*38 = 1/2964
- Anonymous on Oct 26, 2011 Flag Response
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You start with the roulette. You can choose only 6 out of the 38 slots as the dice has only 1-6 numbers. So probability of that is 6/38. Now you can choose only one outcome out of the possible 6 for the dice. so 1/6. For the numbers between 1-6, there are 4 cards each (of different colors) so the probability is 4/52. Do the rest of the math.
- Above on Nov 14, 2011 Flag Response
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The answer is 1/38 * 1/6 * 1/13 * 5 (since 5 numbers, 2-6, can appear in the triplet).
- Viet on Feb 23, 2012 Flag Response

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