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You and a friend are playing a game where a random number X, between 1 to 20 is chosen, and one of you will pick a number and then the other will pick a different number. The one that guesses the closer number wins X dollars. Should you choose to go first, and what number should you choose?
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Assistant Trader

Interviewed at Jane Street

4.4
Aug 7, 2012

You and a friend are playing a game where a random number X, between 1 to 20 is chosen, and one of you will pick a number and then the other will pick a different number. The one that guesses the closer number wins X dollars. Should you choose to go first, and what number should you choose?

Unfair coin with P(H) = 1/3 and P(T) = 2/3. a) How to make an event with 50% probability? b) Expected number of flips until a realization occurs? c) Can you create a strategy to reduce the number of flips necessary? d) Can you create a strategy to reduce the number of flips necessary for an unfair coin with any bias?
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Quant

Interviewed at Jane Street

4.4
Apr 1, 2012

Unfair coin with P(H) = 1/3 and P(T) = 2/3. a) How to make an event with 50% probability? b) Expected number of flips until a realization occurs? c) Can you create a strategy to reduce the number of flips necessary? d) Can you create a strategy to reduce the number of flips necessary for an unfair coin with any bias?

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