- A car has a uniformly distributed value between 0 and 1000. If you bid less than this value, you get nothing but keep your bid. If you bid more than this value, you can sell the car for 1.5 times the value. What should you bid? - The surface of a 3x3 block is painted. The block is split into 27 cubes and one is dropped on the floor. What is the probability that no visible face is painted? If no visible face is painted, what is the probability that it is the centre cube?
1. Digits in 99^20 2. Expected value of dice rolls (20 x 3 vs. 30 x 2). If you were playing a game which one would you pick, or does it not matter? What's the probability that you're going to win?
If the chance of rain on Saturday is 70% and on Sunday is 60%, what is the chance of it raining this weekend?
Have a truck starting that can carry a maximum of 1000 apples, and starts with 2000 apples at a depot. What's the maximum number of apples that can be carried across a 1000 mile desert assuming 1 apple falls off the truck for every mile travelled?
Ask you to find the smallest number that you can not get by using 3,8,20 (or something similar)
if you have a 6 by 6 matrix where each element is either 1 or -1, how many unique matrices are there such that each row and each column multiplies to 1.
If two teams are equally talented, what is the chance that a 7 game series between the two teams reaches the 7th game?
You play a game where you roll a 100-sided die label with the numbers 1-100. You can either get paid the amount rolled in dollars or pay a dollar to roll again. You can always elect to pay another dollar to roll again, until you're finally satisfied with your current roll and get paid out based on that. What's the optimal strategy for this game and what's your expected winnings given this strategy?
Game 1 pays $20 if you flip heads and you flip the coin 4 times, game 2 pays $500 if you flip heads all 4 times. Which game do you pick?
X^4=1, what is X
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