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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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