Assistant Interview Questions

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person A has a 30 sided and person B has a 20 sided die. both players role and the person with the highest role win (on a draw B wins). the loser pays the winner the value of the winners die. 1. calculate expected value of this game for player A (easy) 2. how does this value change if player B can re-roll and when should he re-roll. 3. now how much is it worth for player A to get a re-roll option in this scenario. 4. remove player A reroll. how many re-rolls do player B need in order for him to be a favorite in the game. i believed i solved 4 and 2 I had a decent idea but 3 is very difficult since optimal strategy might change based on opposing players optimal strategy.
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Assistant Trader

Interviewed at Jane Street

4.4
Apr 4, 2014

person A has a 30 sided and person B has a 20 sided die. both players role and the person with the highest role win (on a draw B wins). the loser pays the winner the value of the winners die. 1. calculate expected value of this game for player A (easy) 2. how does this value change if player B can re-roll and when should he re-roll. 3. now how much is it worth for player A to get a re-roll option in this scenario. 4. remove player A reroll. how many re-rolls do player B need in order for him to be a favorite in the game. i believed i solved 4 and 2 I had a decent idea but 3 is very difficult since optimal strategy might change based on opposing players optimal strategy.

You have a dart board thats split in half. If you hit the left half, you get 2 points, if you hit the right half, you get 3 points. If you have an 80% chance of hitting the dart board on any given throw and a 70% chance of hitting the side you're aiming for (given that you hit the dartboard so a 30% chance you hit the side you aren't aiming for), if you have an unlimited number of throws, what's the probability you get a score of exactly 7
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Assistant Trader

Interviewed at Jane Street

4.4
Mar 3, 2014

You have a dart board thats split in half. If you hit the left half, you get 2 points, if you hit the right half, you get 3 points. If you have an 80% chance of hitting the dart board on any given throw and a 70% chance of hitting the side you're aiming for (given that you hit the dartboard so a 30% chance you hit the side you aren't aiming for), if you have an unlimited number of throws, what's the probability you get a score of exactly 7

Two dice - one 10 sided one 6 sided. Guess the roll of the two dice, no penalty for guessing under. You receive the amount on the dice if you guess it. What is the expected value? What is the bet that would maximize your payout?
avatar

Assistant Trader

Interviewed at Jane Street

4.4
Feb 22, 2014

Two dice - one 10 sided one 6 sided. Guess the roll of the two dice, no penalty for guessing under. You receive the amount on the dice if you guess it. What is the expected value? What is the bet that would maximize your payout?

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