Trainee Trader Interview Questions

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Let's say you have 2 regular 6-faced dice. When you throw them down, you know the sum distribution (can vary from 2 to 12). Now let's say you were to erase the numbers on the faces of both the dice, and rewrite them with a new set of positive integers. Can you replicate the same sum distribution? If yes, how?
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Assistant Trader

Interviewed at Jane Street

4.4
Jul 11, 2011

Let's say you have 2 regular 6-faced dice. When you throw them down, you know the sum distribution (can vary from 2 to 12). Now let's say you were to erase the numbers on the faces of both the dice, and rewrite them with a new set of positive integers. Can you replicate the same sum distribution? If yes, how?

73 - 227? What's the probability that it rains on at least one of Saturday or Sunday if Saturday has a 60% chance of rain and Sunday has a 70% chance of rain? You have 2 fairly weighted dice. You and an opponent pick any integer one after the other. If your number is closer to the sum of the faces on the rolled dice, you win. Do you want to go first and what number do you choose? What's the probability of winning? You have 27 cubes with all faces painted white. You put them together into a 3x3x3 cube and paint the exterior blue. After breaking it back up, you pick a cube and put it on the table and the five visible faces are all white. What's the probability the non visible face is blue?
avatar

Assistant Trader

Interviewed at Jane Street

4.4
Oct 22, 2015

73 - 227? What's the probability that it rains on at least one of Saturday or Sunday if Saturday has a 60% chance of rain and Sunday has a 70% chance of rain? You have 2 fairly weighted dice. You and an opponent pick any integer one after the other. If your number is closer to the sum of the faces on the rolled dice, you win. Do you want to go first and what number do you choose? What's the probability of winning? You have 27 cubes with all faces painted white. You put them together into a 3x3x3 cube and paint the exterior blue. After breaking it back up, you pick a cube and put it on the table and the five visible faces are all white. What's the probability the non visible face is blue?

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