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Assistant trader Interview Questions

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Here is an example of a brainteaser during the interview: You have five pirates, ranked from 5 to 1 in descending order. The top pirate has the right to propose how 100 gold coins should be divided among them. But the others get to vote on his plan, and if fewer than half agree with him, he gets killed. How will the coins end up being divided, assuming all the pirates are rational and want to end up alive?

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If the pirates are RATIONAL- then they would all agree with taking just 20 coins a peice and splitting it evenly. That is the short and sweet answer. Unfortunately these nerd interviewers may prefer a pointlessly long and drawn out answer to demonstrate your irrelevant mathematical reasoning skills/ability In which case you may answer with the following Give one coin each to the 2 lowest ranked pirates. and split the remaining between the top 3( Maybe 32 for the top pirate and 33 for pirate 2 and 3 ). The bottom 2 will certainly vote against you- but now atleast you are increasing your odds of the other 2 pirates agreeing with the plan. ( which are the 2 minimum votes needed for pirate one to survive) Obvious explanation If there are 5 pirates, one comes up with the plan and the other 4 vote. If fewer then half agree with the top pirate- he gets killed. That means if less than 2 agree he would get killed. He need at the minimum 2 pirates to agree with him to live.

the answer isnt that obviouse.....you give the 3rd and 1st one coin and keep 98....start at the beginning. if theres 2 pirates, 100 for 2, 0 for 1 (one doesnt like this) If there is three 1 will be happy with just a single coin, b/c he does not want it to go down to 2. If there is 4 pirates, 2 will be happy with a single coin, b/c he does not want it to get down to 3 pirates where he will receive 0. So he gets 1 and 4 gets 99. At 5 it changes a bit. Here 1 and 3 will be happy with single coins b/c if it goes down to 4 they will receive 0 coins. So 5 takes 98, and 1 and 3 take 1 one each

Flip a coin until either HHT or HTT appears. Is one more likely to appear first? If so, which one and with what probability?

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If you flip a coin until you decide to stop and you want to maximize the ratio of heads to total flips, what is that expected ratio?

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Simulate a 6 sided die with a coin.

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You have a box filled with cash. Cash value is uniformly randomly distributed from 1 to 1000. You are trying to win the box in an auction: you win the box if you bid at least the value of the cash in the box; you win nothing if you bid less (but you lose nothing). If you win the box, you can resell it for 150% of its value. How much should you bid to maximize the expected value of your profit (resale of box minus bid)?

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what is the expected number of flips of a coin to simulate a 6 sided die.

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There is a 91% chance of seeing a shooting star in the next hour, what is the probability of seeing a shooting star in the next half hour?

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What is the expected value of rolling two dice?

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Toss 4 coins - probability of more than 2 heads - expected winnings if $1 for each heads - expected winnings if can re-toss 1 coin if chosen 1 20 sided die - player A and B both choose a number. Whoever's number closest to value of the die wins the amount on the die. - optimal strategy? do you want to go first? - what is the expected winnings?

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You are standing beside a road watching cars pass by. The probability that you see a car pass by in 1 minute is 1/4. What is the probability that you see a car pass by in 30 seconds?

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