Flip a coin until either HHT or HTT appears. Is one more likely to appear first? If so, which one and with what probability?
Trade Operations Interview Questions
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In world series (baseball) there are two teams, A and B. You know that each can win 50% of the time (1:1 odds). You also know how the game works, i.e. Whoever wins 4 games first wins. What is the probability of getting to game 7 (i.e. Each team wins 3 games)?
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.
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?
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 you roll a fair coin 10 times what is the expected product of number of heads and number of tails?
Let's play a game - I give you a 12 sided die and will pay you whatever the die lands on. If you are unhappy with the roll, you can choose to roll another two 6-sided dice and I wil pay you the sum of the two dice. How much are you willing to pay to play this game.
We consider numbers from 1 to 1 million. How many digits 2 are there??
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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