Intern Interview Questions

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I'm flipping three coins. If all three are the same (all heads or all tails) then I will get 10 dollars and I may finish the game. If it is not the case then I might ask to flip any number of the coins again (to flip one of them or two of them again, etc.). What's the expected gain by playing this game?
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Intern

Interviewed at Jane Street

4.4
May 6, 2018

I'm flipping three coins. If all three are the same (all heads or all tails) then I will get 10 dollars and I may finish the game. If it is not the case then I might ask to flip any number of the coins again (to flip one of them or two of them again, etc.). What's the expected gain by playing this game?

Question 2: A chest contains a treasure that is equally likely to be worth any amount between $0 and $1,000. You may bid on the chest, but you only get it if you bid more than the value of the treasure, x. You can resell the treasure for 1.5x. What should you bid?
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Assistant Trader Intern

Interviewed at Jane Street

4.4
Apr 15, 2013

Question 2: A chest contains a treasure that is equally likely to be worth any amount between $0 and $1,000. You may bid on the chest, but you only get it if you bid more than the value of the treasure, x. You can resell the treasure for 1.5x. What should you bid?

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