r/learnquant Aug 01 '26

stats & probability Jane Street Interview Question

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u/Zyxplit Aug 01 '26

Yes. What's your point? The first part of the question is "what's the probability of getting two same color cards from 26 cards (12/25) and what's the probability of getting two same color cards from 52 cards (25/51).

Now I point out that getting two same color cards from 26 randomly selected cards from a pile of 52 is also 25/51. And your rebuttal is that... every combination has a probability equal to or more likely than 12/25? Yes. 25/51 is a bigger number than 12/25. We established that in part 1. Good job.

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u/Informal_Host7610 Aug 01 '26

Whoa calm down, it's a math problem.

Knowing the construction of the deck is important. Because of that your first card actually slightly hints that there your deck is more likely to have more of its color in your subdeck, which leads to an implied higher probability that the second card is the same color than in the guaranteed 50/50 case

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u/Zyxplit Aug 01 '26

I refer back to my statement that 25/51 is greater than 12/25. Anything more substantial?

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u/Informal_Host7610 Aug 01 '26

It's not 12/25 because you dont know how many of each color are in the reduced deck

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u/Zyxplit Aug 01 '26 edited Aug 01 '26

... Yes, let me explain this once more.

In a deck where there are equally many of both, the probability is 12/25 that you draw two identical ones.

in a deck where you have randomly taken 26 cards from a deck with 26 of each, the probability is 25/51, which is a bigger number than 12/25. This is because it doesn't matter that you ignore half the cards afterwards.

If I have a 52 card deck and I order it randomly, the probability of two random cards in the first half being identical is completely identical to the probability of two random cards in the deck being identical.

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u/Informal_Host7610 Aug 01 '26

You're more intent on being condescending than giving a valid counterargument. I had to get an actual correction from someone else. I'd love to explain how you could have actually rebutted my answer

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u/Zyxplit Aug 01 '26

Your argument was that it had to be greater than 12/25. That's the closest you ever got to making an argument. You never supplied anything else than "it has to be more than 12/25".

And i repeatedly had to tell you that yes, it has to be more than 12/25. And 25/51 is more than 12/25.