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Trader Interview Questions

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was asked this question today...you want buy a car at an auction whos price is uniformly distributed between 0-1000 if you bid more than the car you win it at the price you bid.if you bid less that the cars proce you dont win it but dont lose anything. you can sell the car for 1.5 time the value of which you bought it. what should you bid on the car to maximumise your profit?

11 Answers

i told the interviewer that the expected value is negitve so you should bid 0 to maximum your profit.(0 is greater that any negitive number) but the answer which i was guided towards wasE(X)= X-(X/2)*1.5 letting X = your bid so if you bid 500 E(x) = 500 - 250(1.5) = 125 pretty weird question if you ask me. comming up with a formula for expected value when i was orgionaly asked what would be my bid to maxiumise my profit. any1 have an thoughts? maybe this was obvious?

If you bid X then your expected gain is (X/2)*1.5 So (X/2)*1.5 - X should be your profit... I.E. negative expected value. Could it be the interview just wanted to see how you can mathematically back up your original statement?

yeah good point! that is most likely what he was testing. i suppose i just assumed it was obviously neg EV.

We consider numbers from 1 to 1 million. How many digits 2 are there??

10 Answers

You roll two die: What is the probability of rolling a 10 and an 11 before rolling a 7?

8 Answers

If I write down all of the numbers from 1 to 1,000,000 on a page, how many times do I write down the digit 2?

9 Answers

If there was a drawer in front of me containing 4 socks, either black or white, and I know that I have a 50% probability of pulling out two white socks in a row, then what is the probability of pulling out two black socks?

5 Answers

Pretty standard question that has been asked before... keep flipping a coin until a winning combination appears (either HHT or HTT). Which strategy would you pick given the choice and why. Find the probabilities of winning associated with each strategy.

5 Answers

n unbiased coins. What is the probability that half of them exactly are heads. Answer the question for n= 2, 3, 20000

6 Answers

2 fair dice. What is the probability of both showing six if I have observed at least one six.

6 Answers

If you extend the faces of a tetrahedron as planes infinitely in all directions, how many regions does this divide 3D space into?

5 Answers

A seller is selling you a car whose value is uniformly distributed between 0 and 1000 but you don’t know the real value and you need to bid for the car. If your bid price is higher than the its real value, the deal will be done at your bid price and you can afterwards resell the car elsewhere for 1.5 times its real value. Otherwise, the deal will not be done. You can only bid once. What will be your optimal bid price?

4 Answers
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