There are 25 horses. Each time you can race 5 horses together. Now you need to pick the top three horses among them. How many races do you need to conduct?
Trader Intern Interview Questions
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Given a 12 sided dice, you roll the dice repeatedly until the cumulative sum is odd. What is the number of the cumulative sum you can have with the highest probability?
During the third interview : imagine an infinite chess board. If the horse from 1 case, in how many cases can he possibly ends after 10 moves. You actually don't have to give a number but a 95% confidence interval. pen and paper allowed
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?
what is the expected number of flips of a coin to simulate a 6 sided die.
If we flip a coin 100 times, what is the probability of getting even number of heads?
A bad king has 1000 bottles of wine. A neighboring king plots to kill the bad king, and sends a servant to poison the wine. the servant is able to poison only one of them before he is caught. The guards don't know which bottle was poisoned, but they do know that the poison is so potent that even if it was diluted 1,000,000 times, it would still be fatal. Furthermore, the effects of the poison take one month to surface. The king decides he will get some of his prisoners in his vast dungeons to drink the wine. At a minimum how many servants does he need to kill to find out the poisioned bottle of wine and will still be able to drink the rest of the wine in 5 weeks time?
Is it possible to change the numbers on two six sided dice to other positive numbers so that the probability distribution of their sum remains unchanged?
person A has a 30 sided and person B has a 20 sided die. both players role and the person with the highest role win (on a draw B wins). the loser pays the winner the value of the winners die. 1. calculate expected value of this game for player A (easy) 2. how does this value change if player B can re-roll and when should he re-roll. 3. now how much is it worth for player A to get a re-roll option in this scenario. 4. remove player A reroll. how many re-rolls do player B need in order for him to be a favorite in the game. i believed i solved 4 and 2 I had a decent idea but 3 is very difficult since optimal strategy might change based on opposing players optimal strategy.
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?
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