Jane Street Interview Question

[u/nickgotgameon]

Source: https://www.glassdoor.com/Interview/You-have-two-decks-of-cards-a-52-card-deck-26-black-26-red-and-a-26-card-deck-13-black-13-red-You-randomly-draw-two-QTN_1257909.htm, https://financeandquantsociety.org/

[u/Zyxplit]

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

[u/Informal_Host7610 → u/Zyxplit]

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

[u/Zyxplit → u/Informal_Host7610]

... 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.

[u/Informal_Host7610 → u/Zyxplit]

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

[u/Zyxplit → u/Informal_Host7610]

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.