Intern Interview Questions

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The interviewer gives you 100 blank cards, and you can write a single positive integer on each card. The interviewer looks at the cards when you're done (so he knows the probability distribution of the deck), then shuffles the deck. The interviewer guesses the top card of the deck, and if he's right, he makes in $ the number written on the card. What numbers should you write on the cards to minimize the expected return of the interviewer?
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Trading Intern

Interviewed at Jane Street

4.4
Apr 23, 2014

The interviewer gives you 100 blank cards, and you can write a single positive integer on each card. The interviewer looks at the cards when you're done (so he knows the probability distribution of the deck), then shuffles the deck. The interviewer guesses the top card of the deck, and if he's right, he makes in $ the number written on the card. What numbers should you write on the cards to minimize the expected return of the interviewer?

2) A. 10 ropes, each one has one red end and one blue end. Each time, take out a red and a blue end, make them together. Repeat 10 times. The expectation of the number of loops. B. 10 ropes, no color. All the other remains the same.
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Quantitative Researcher Summer Intern

Interviewed at Jane Street

4.4
Apr 18, 2011

2) A. 10 ropes, each one has one red end and one blue end. Each time, take out a red and a blue end, make them together. Repeat 10 times. The expectation of the number of loops. B. 10 ropes, no color. All the other remains the same.

You are playing a game in which four fair coins are flipped and the amount of money you receive in dollars is equal to the number of heads that appear in total. If you do not like the outcome of the first four flips, you have the option to re-flip the four coins, but you are obligated to take the second outcome. Determine a fair value fr the game.
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Trader Intern

Interviewed at Jane Street

4.4
Jan 30, 2012

You are playing a game in which four fair coins are flipped and the amount of money you receive in dollars is equal to the number of heads that appear in total. If you do not like the outcome of the first four flips, you have the option to re-flip the four coins, but you are obligated to take the second outcome. Determine a fair value fr the game.

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