1. Probability and Statistics - Creating triangles
What is the probability of creating an acute-angled triangle?
2. Probability and Statistics - Point on a disc
What is the expected distance from the center for a point chosen at random inside a unit circle?
3. Probability and Statistics - Bullseye
In a bullseye game, if you hit within a 1cm radius, you score 50 points, and if you hit between 1cm and 2cm radius, you score 30 points. What is the expected score?
4. Expected Maximum of n Uniformly Distributed Variables
What is the expected maximum value of n independent and identically distributed variables uniformly distributed between 0 and 1?
5. Probability of Drawing a Gold Coin
Starting with x gold coins and y silver coins in a bag, if you draw one coin at random and then replace it with a gold coin, what is the probability of drawing a gold coin after k draws?