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You have been chosen to play a game involving a 6-sided die. You get to roll the die once, see the result, and then may choose to either stop or roll again. Your payoff is the sum of your rolls, unless this sum is (strictly) greater than 6, in which case you "bust" and get nothing. What is your strategy for this game? That is, for each possible outcome of the first roll will you choose to stop or to roll again? Why?
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Summer Intern

Interviewed at Jane Street

4.4★
Dec 26, 2014

You have been chosen to play a game involving a 6-sided die. You get to roll the die once, see the result, and then may choose to either stop or roll again. Your payoff is the sum of your rolls, unless this sum is (strictly) greater than 6, in which case you "bust" and get nothing. What is your strategy for this game? That is, for each possible outcome of the first roll will you choose to stop or to roll again? Why?

We have two urns. You can't tell them apart from the outside, but one has three $1 chips and seven $10 chips, and the other has eight $1 chips and two $10 chips. You randomly draw a chip from one of the urns and it happens to be a $10 chip. Without replacing this draw, I offer you a chance to draw and keep a chip from either urn. Should you draw from the same urn or the opposite urn, and what is the expected value of the chip you draw? Why?
avatar

Summer Intern

Interviewed at Jane Street

4.4★
Dec 26, 2014

We have two urns. You can't tell them apart from the outside, but one has three $1 chips and seven $10 chips, and the other has eight $1 chips and two $10 chips. You randomly draw a chip from one of the urns and it happens to be a $10 chip. Without replacing this draw, I offer you a chance to draw and keep a chip from either urn. Should you draw from the same urn or the opposite urn, and what is the expected value of the chip you draw? Why?

Suppose you are given the opportunity to bid for a treasure chest, which you know to be priced uniformly anywhere between £0-£1000. If you bid equal to or above the price, you win the treasure chest (at the cost of your bid). If you bid below the price, you do not earn the treasure chest. Now, also suppose you can sell the treasure chest for 1.5 times the price of the treasure chest (should you obtain the chest). What should your bid be?
avatar

Summer Internship

Interviewed at Jane Street

4.4★
Apr 27, 2012

Suppose you are given the opportunity to bid for a treasure chest, which you know to be priced uniformly anywhere between £0-£1000. If you bid equal to or above the price, you win the treasure chest (at the cost of your bid). If you bid below the price, you do not earn the treasure chest. Now, also suppose you can sell the treasure chest for 1.5 times the price of the treasure chest (should you obtain the chest). What should your bid be?

conditional probability questions: there is a test to test one's IQ. If your IQ is x, you will get a score between x-10 to x+10. Now someone's score is 150. What's his IQ range? Can you tell the best estimate? If not, what else condition you need?
avatar

Strats and Modeling Summer Intern

Interviewed at Morgan Stanley

3.9★
Mar 20, 2014

conditional probability questions: there is a test to test one's IQ. If your IQ is x, you will get a score between x-10 to x+10. Now someone's score is 150. What's his IQ range? Can you tell the best estimate? If not, what else condition you need?

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