Trading Associate Interview Questions

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On the island, there are 99 lions and one sheep. When lion eats sheep, he transforms into a sheep. Lion's primary target is to survive, secondly he wants to eat a sheep. Suppose that all lions are intelligent. How many lions will be on the island after some time?
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Trading

Interviewed at Jane Street

4.4
Aug 1, 2016

On the island, there are 99 lions and one sheep. When lion eats sheep, he transforms into a sheep. Lion's primary target is to survive, secondly he wants to eat a sheep. Suppose that all lions are intelligent. How many lions will be on the island after some time?

Phone interview 1) Question 1. a) I have toss 10 fair coins. What is the probability of an even number of heads. b) Now 100 fair coins. c) Now X unfair coins and Y fair coins. Question 2) I have a 3x3 Grid and in each cell I place a lightbulb. Each of the 9 lightbulbs is then turned on with probability 1/2. What is the probability that there are NO adjacent cells both lit up. Phone Interview 2) Question 1a) We are playing a game with a coin. I get to either decide heads or tails and you then get to be the other. (i.e i pick tails so you are heads) The coin is tossed until someone reaches 5 of their face. I.e 5 Heads. That person wins. Im going to toss the coin once then let you decide what you want to be. What is your probability of winning . (to make this clear if i toss the coin first, its a head then you decide to be heads you now only need 4 more heads to win whereas i still need 5 tails) Question 1b) Now instead of coins we play the same game with cards. So you must select a suit (Spades, Hearts, Diamonds, Clubs) and we turn over cards (without replacement) until someone has seen 5 of their suit. Same thing. Now I let you decide, would you like to pick your suit right away, after I show 1 card, or after I show 2 cards. Which of these 3 options gives you the best chance of winning. Question 2a) Its a game between you and a very silly opponent. You both get a chance to select a random number 1-100 (inclusive) and your opponent guesses uniformly randomly. You don't know what the opponent has selected. Then the person with the lowest number wins and the looser pays them their guess. I.e you guess 45 and the opponent guesses 56 then he owes you £45. Question 2b) The game is now changed slightly and we add a third opponent however he is logical and intelligent and will play optimally. Its now you, the idiot and the clever clogs. What do you guess as your number. Phone interview 3) This interview only had 1 question but its a long one. You roll a dice and I roll a dice. The total sum of our rolls is put into a box. I.e you roll 4 and I roll 5 we put £9 into a box. We then take it in turns to bid for the money in this box. How should you play? Onsite Interview 1) Making markets on 4 cards. I was told to make markets 4 wide on all of these. You should read their guide on making markets if you don't know what that means (https://www.janestreet.com/static/pdfs/trading-interview.pdf?utm_source=web&utm_medium=pdf&utm_campaign=probability_markets_guide) I was told to make markets on the following: Sum of black cards. Number of red cards squared. Highest card. 10/number of clubs. Lowest Black card. Sum of even cards. You then were given fair 1:1 bets on a roulette you could make to hedge and insure yourself. Like putting down 5 chips on red that would pay out 5 on a red card. Onsite interview 2) This was done as a simulation on excel It might be hard to try and do this one yourself but try to think about some strategies . We have 10 bias coins. They are normally distributed with mean 0.5 of being heads. i.e some coins will flip heads 10% and some 90% but their average is 0.5 You get given 100 flips and get paid £1 for each heads. So you could flip each of the coin 10 times or maybe just flip 2 coins each 50 times or any other strategy , its about seeing what coins come up heads more . Onsite interview 3) Question 1a) I get out all 13 Hearts Ace - King. I lay them face down. We treat the Jack , Queen and King as 0 for this . You then get to pay me £1 to ask the difference of any two cards. You can do this as much as you like with any pair of cards. So lets say you asked for the difference of card 2 and 3 and I have a look at them and see they are the King and 7 I would then tell you "the difference is 7". You then get to at any time. select 2 cards and get paid the product of them. So you can say " product of card 5 and card 7" lets say they are the 8 and 5 then I would pay you £40. How much would you pay to play this game ? Whats your optimal strategy . Question 1b) We now remove the King and Queen and leave only the Jack so you have 11 cards. of value 0-10 . now how much do you pay ? Make me a market 10 wide on this game. Onsite Interview 4) Question 1) This was by far the worst one for me, I was worn out and tired after a long day so I cannot remember anything of value about it i'm afraid. It was another excel simulation.
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Quantitate Trading

Interviewed at Jane Street

4.4
Sep 22, 2020

Phone interview 1) Question 1. a) I have toss 10 fair coins. What is the probability of an even number of heads. b) Now 100 fair coins. c) Now X unfair coins and Y fair coins. Question 2) I have a 3x3 Grid and in each cell I place a lightbulb. Each of the 9 lightbulbs is then turned on with probability 1/2. What is the probability that there are NO adjacent cells both lit up. Phone Interview 2) Question 1a) We are playing a game with a coin. I get to either decide heads or tails and you then get to be the other. (i.e i pick tails so you are heads) The coin is tossed until someone reaches 5 of their face. I.e 5 Heads. That person wins. Im going to toss the coin once then let you decide what you want to be. What is your probability of winning . (to make this clear if i toss the coin first, its a head then you decide to be heads you now only need 4 more heads to win whereas i still need 5 tails) Question 1b) Now instead of coins we play the same game with cards. So you must select a suit (Spades, Hearts, Diamonds, Clubs) and we turn over cards (without replacement) until someone has seen 5 of their suit. Same thing. Now I let you decide, would you like to pick your suit right away, after I show 1 card, or after I show 2 cards. Which of these 3 options gives you the best chance of winning. Question 2a) Its a game between you and a very silly opponent. You both get a chance to select a random number 1-100 (inclusive) and your opponent guesses uniformly randomly. You don't know what the opponent has selected. Then the person with the lowest number wins and the looser pays them their guess. I.e you guess 45 and the opponent guesses 56 then he owes you £45. Question 2b) The game is now changed slightly and we add a third opponent however he is logical and intelligent and will play optimally. Its now you, the idiot and the clever clogs. What do you guess as your number. Phone interview 3) This interview only had 1 question but its a long one. You roll a dice and I roll a dice. The total sum of our rolls is put into a box. I.e you roll 4 and I roll 5 we put £9 into a box. We then take it in turns to bid for the money in this box. How should you play? Onsite Interview 1) Making markets on 4 cards. I was told to make markets 4 wide on all of these. You should read their guide on making markets if you don't know what that means (https://www.janestreet.com/static/pdfs/trading-interview.pdf?utm_source=web&utm_medium=pdf&utm_campaign=probability_markets_guide) I was told to make markets on the following: Sum of black cards. Number of red cards squared. Highest card. 10/number of clubs. Lowest Black card. Sum of even cards. You then were given fair 1:1 bets on a roulette you could make to hedge and insure yourself. Like putting down 5 chips on red that would pay out 5 on a red card. Onsite interview 2) This was done as a simulation on excel It might be hard to try and do this one yourself but try to think about some strategies . We have 10 bias coins. They are normally distributed with mean 0.5 of being heads. i.e some coins will flip heads 10% and some 90% but their average is 0.5 You get given 100 flips and get paid £1 for each heads. So you could flip each of the coin 10 times or maybe just flip 2 coins each 50 times or any other strategy , its about seeing what coins come up heads more . Onsite interview 3) Question 1a) I get out all 13 Hearts Ace - King. I lay them face down. We treat the Jack , Queen and King as 0 for this . You then get to pay me £1 to ask the difference of any two cards. You can do this as much as you like with any pair of cards. So lets say you asked for the difference of card 2 and 3 and I have a look at them and see they are the King and 7 I would then tell you "the difference is 7". You then get to at any time. select 2 cards and get paid the product of them. So you can say " product of card 5 and card 7" lets say they are the 8 and 5 then I would pay you £40. How much would you pay to play this game ? Whats your optimal strategy . Question 1b) We now remove the King and Queen and leave only the Jack so you have 11 cards. of value 0-10 . now how much do you pay ? Make me a market 10 wide on this game. Onsite Interview 4) Question 1) This was by far the worst one for me, I was worn out and tired after a long day so I cannot remember anything of value about it i'm afraid. It was another excel simulation.

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