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You have a drawer with an infinite number of two colors of socks, which exist in equal probability. What is the expected number of attempts at taking out socks individually from the drawer before a matching pair is found?
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Quantitative Trader Intern

Interviewed at Jane Street

4.4★
Sep 18, 2019

You have a drawer with an infinite number of two colors of socks, which exist in equal probability. What is the expected number of attempts at taking out socks individually from the drawer before a matching pair is found?

I did initially misunderstand this question and had to be helped along, but it is fairly difficult to do on the fly anyway: "We're playing a game with an unbiased 30-sided die. Before we roll, we both pick (distinct) numbers between 1 and 30, and then we roll the die. If the number that appears is closer to the number I picked, you pay me, in dollars, the number on the die; if it is closer to the number you picked, I pay you, in dollars, the number on the die; if it is equidistant we do nothing. What's the optimal strategy - do you go first or second, and how do you pick your number? What's your expectation?"
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Assistant Trader

Interviewed at Jane Street

4.4★
Mar 25, 2014

I did initially misunderstand this question and had to be helped along, but it is fairly difficult to do on the fly anyway: "We're playing a game with an unbiased 30-sided die. Before we roll, we both pick (distinct) numbers between 1 and 30, and then we roll the die. If the number that appears is closer to the number I picked, you pay me, in dollars, the number on the die; if it is closer to the number you picked, I pay you, in dollars, the number on the die; if it is equidistant we do nothing. What's the optimal strategy - do you go first or second, and how do you pick your number? What's your expectation?"

The interview started and I was told to not use and pencil or paper. They asked me some squaring questions and some subtraction with large numbers. I was also asked how much I would pay to play a game where I get heads if I win a dollar, and how much I would be willing to pay if I was able to re-flip up to two more times.
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Assistant Trader Internship

Interviewed at Jane Street

4.4★
Feb 19, 2014

The interview started and I was told to not use and pencil or paper. They asked me some squaring questions and some subtraction with large numbers. I was also asked how much I would pay to play a game where I get heads if I win a dollar, and how much I would be willing to pay if I was able to re-flip up to two more times.

Given a fair die 1-6, what would be the expected value of the result? What if you have two chances? After the first row, you can choose whether or not you want to keep it. What would be the maximum expected value based on the best strategy.
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Quantitative Trader

Interviewed at Jane Street

4.4★
Oct 10, 2015

Given a fair die 1-6, what would be the expected value of the result? What if you have two chances? After the first row, you can choose whether or not you want to keep it. What would be the maximum expected value based on the best strategy.

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