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was asked this question 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?

12 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.

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?

10 Answers

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

10 Answers

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

6 Answers

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

6 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

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?

6 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

If I role a dice and can keep the value on the dice face up, what should my strategy be if I can have more than one role and can keep the value of all the roles but if I go 7 or above I go bust.

5 Answers

If I choose randomly 6 numbers from a list of the first 12 prime numbers, then what is the probability that the sum of those six numbers will odd?

6 Answers
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